Details

analyze354.0ms (0.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	50%	0.1%	0%	50%	0%	2
0%	0%	50%	0.1%	0%	50%	0%	3
0%	0%	50%	0.1%	0%	50%	0%	4
25%	12.5%	37.5%	0.1%	0%	50%	0%	5
26.7%	12.5%	34.3%	0.1%	0%	53.1%	0%	6
37%	15.6%	26.5%	0.1%	1.6%	54.6%	1.6%	7
40.8%	15.6%	22.6%	0.1%	2.3%	57%	2.3%	8
49.4%	17.2%	17.6%	0.1%	3.5%	58.1%	3.5%	9
53.3%	17.2%	15%	0.1%	4.1%	59.5%	4.1%	10
59.5%	18%	12.2%	0.1%	4.8%	60.2%	4.8%	11
62.5%	18%	10.8%	0.1%	5.1%	60.9%	5.1%	12

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample11.1s (28.5%)

Results

4.9s	8256×	body	256	valid
3.4s	1362×	body	1024	invalid
1.2s	713×	body	512	invalid
1.1s	1585×	body	256	invalid
271.0ms	516×	body	256	infinite
248.0ms	248×	body	256	unsamplable

Bogosity

preprocess297.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

1272×	`rational_best-simplify-55`
1228×	`exponential-simplify-27`
1068×	`rational_best-simplify-1`
992×	`rational_best-simplify-108`
776×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	98
1	52	98
2	100	98
3	212	86
4	493	86
5	1567	86
6	4539	86
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (.f64 k (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))))
(.f64 1 (/.f64 (pow.f64 (.f64 k (*.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))) (sqrt.f64 n)))
(/.f64 (pow.f64 (.f64 k (.f64 2 (PI.f64))) (-.f64 1/2 (/.f64 n 2))) (sqrt.f64 n))
(/.f64 (pow.f64 (.f64 2 (.f64 k (PI.f64))) (-.f64 1/2 (/.f64 n 2))) (sqrt.f64 n))

Compiler

Compiled 20 to 17 computations (15% saved)

simplify217.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1472×	`exponential-simplify-26`
1194×	`rational_best-simplify-80`
1006×	`rational_best-simplify-63`
710×	`rational_best-simplify-47`
650×	`rational_best-simplify-103`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	34	49
2	59	49
3	117	43
4	260	43
5	807	43
6	2311	43

Stop Event

1×	node limit

Counts

1 → 5

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Outputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (-.f64 1/2 (/.f64 k 2))))
(.f64 1 (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (/.f64 k 2))) (sqrt.f64 k))

eval2.0ms (0%)

Compiler: Compiled 78 to 54 computations (30.8% saved)

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	3	6

Error

0.3b

Counts

6 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
▶	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize94.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
✓	0.2b	(.f64 (.f64 2 (PI.f64)) n)
✓	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

Compiler

Compiled 56 to 38 computations (32.1% saved)

series243.0ms (0.6%)

Counts

4 → 48

Calls

18 calls:

Time	Variable		Point	Expression
118.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
94.0ms	n	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
11.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
11.0ms	k	@	-inf	(/.f64 1 (sqrt.f64 k))
4.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite346.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1226×	`rational_best-2`
1226×	`rational_best-3`
1226×	`rational_best-1`
1220×	`rational_best-4`
1220×	`exponential-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	108
1	120	102
2	265	102
3	758	102
4	3054	102

Stop Event

1×	node limit

Counts

4 → 121

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (sqrt.f64 k))
(.f64 (.f64 2 (PI.f64)) n)
(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)) (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) (.f64 (sqrt.f64 k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 k) 2) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) (.f64 (sqrt.f64 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 4)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 2) (/.f64 (sqrt.f64 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4) (.f64 (sqrt.f64 k) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 8 (sqrt.f64 k))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 4) (.f64 2 (.f64 (sqrt.f64 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 4 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4)) (.f64 4 (.f64 (sqrt.f64 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 4 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 2)) (/.f64 1/2 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 1/2) (.f64 (sqrt.f64 k) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 1/2) (.f64 (sqrt.f64 k) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) -2) (neg.f64 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 4 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4)) (.f64 (sqrt.f64 k) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) 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simplify616.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1210×	`rational_best-simplify-49`
1208×	`rational_best-simplify-52`
1204×	`rational_best-simplify-53`
1102×	`rational_best-simplify-63`
584×	`rational_best-simplify-108`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	6655
1	937	6573
2	5333	6527

Stop Event

1×	node limit

Counts

169 → 183

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) 0)
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(+.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) 0)
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(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) (.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) 1)
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 k) 2) (sqrt.f64 k)))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) (.f64 (sqrt.f64 k) 2))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 2) (/.f64 (sqrt.f64 k) 2))
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(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) 4)
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 8 (sqrt.f64 k))) 8)
(/.f64 (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 4) (.f64 2 (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 4 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4)) (.f64 4 (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4)) 16)
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k)))
(/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 4 (sqrt.f64 k)))
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(/.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) 4) (/.f64 1 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) 8) (/.f64 1/2 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))) 2)
(/.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 1 (*.f64 (sqrt.f64 k) 4))) 4)
(/.f64 (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 4 (sqrt.f64 k))) 1/4)
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) 2)
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) 2) (/.f64 1 (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) 4) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) 8) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))) 4)
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 1 (.f64 (sqrt.f64 k) 4))) 8)
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 4 (sqrt.f64 k))) 1/2)
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k)) 2) (/.f64 2 (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 2)) (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 2))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (+.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 4)) (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 4))) (/.f64 1/2 (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) 1)
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(+.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k)))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) 2))
(*.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 1 (sqrt.f64 k)) 1)
(*.f64 2 (/.f64 1/2 (sqrt.f64 k)))
(*.f64 1/2 (/.f64 2 (sqrt.f64 k)))
(.f64 4 (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(.f64 8 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)))
(*.f64 (/.f64 2 (sqrt.f64 k)) 1/2)
(*.f64 1/4 (/.f64 4 (sqrt.f64 k)))
(*.f64 (/.f64 1/2 (sqrt.f64 k)) 2)
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) 4)
(*.f64 (/.f64 4 (sqrt.f64 k)) 1/4)
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) 8)
(pow.f64 (/.f64 1 (sqrt.f64 k)) 1)
(+.f64 (.f64 2 (.f64 (PI.f64) n)) 0)
(+.f64 0 (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(-.f64 (.f64 2 (.f64 (PI.f64) n)) 0)
(-.f64 (.f64 (PI.f64) n) (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2))
(/.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(/.f64 (.f64 n (.f64 (PI.f64) 8)) 4)
(/.f64 (.f64 n (.f64 2 (*.f64 (PI.f64) 8))) 8)
(/.f64 (.f64 (.f64 n 4) (*.f64 (PI.f64) 8)) 16)
(/.f64 (+.f64 (.f64 n (.f64 2 (.f64 (PI.f64) 8))) (.f64 n (.f64 2 (.f64 (PI.f64) 8)))) 16)
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1)
(+.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 0)
(+.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 2))
(+.f64 (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 2)) (fabs.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 2)))
(-.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 0)
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 2) (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 2))
(.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))))
(.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 1)
(.f64 1/2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
(.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 1/2)
(.f64 (pow.f64 2 (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (/.f64 k -2))))
(*.f64 (pow.f64 (PI.f64) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (+.f64 n n) (+.f64 1/2 (/.f64 k -2))))
(.f64 1/4 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) 2) (*.f64 2 (pow.f64 n (+.f64 1/2 (/.f64 k -2)))))
(.f64 (.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2)))) (/.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) 2))
(.f64 (.f64 2 (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) 2))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4) 1/4)
(.f64 (pow.f64 n (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/4 (/.f64 k -4))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/4 (/.f64 k -4))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (/.f64 k -2))) (pow.f64 2 (+.f64 1/2 (/.f64 k -2))))
(*.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (PI.f64) (+.f64 1/2 (/.f64 k -2))))
(.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/4 (/.f64 k -4)))) (pow.f64 n (+.f64 1/4 (/.f64 k -4))))
(.f64 (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))
(.f64 (/.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) 2) (.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2)))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k -2)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) 4) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (/.f64 n 2) (+.f64 1/2 (/.f64 k -2))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))))
(.f64 (pow.f64 (/.f64 n 2) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 (PI.f64) 4) (+.f64 1/2 (/.f64 k -2))))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 1)
(/.f64 (.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 2)
(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4) 4)
(/.f64 (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 4) 8)
(fabs.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
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(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
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(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
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(*.f64 (/.f64 2 (sqrt.f64 k)) 1/2)
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(*.f64 (/.f64 1/2 (sqrt.f64 k)) 2)
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(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 1 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 1)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 1/2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 1/2)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 2 (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(*.f64 (pow.f64 (PI.f64) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (+.f64 n n) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 1/4 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (/.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) 2) (*.f64 2 (pow.f64 n (+.f64 1/2 (/.f64 k -2)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2)))) (/.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (.f64 2 (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) 2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4) 1/4)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 n (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (pow.f64 n (+.f64 1/4 (/.f64 k -4))) (pow.f64 n (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/4 (/.f64 k -4))) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/4 (/.f64 k -4))))
(pow.f64 (.f64 (.f64 (PI.f64) (.f64 n 2)) (.f64 (PI.f64) (*.f64 n 2))) (+.f64 1/4 (/.f64 k -4)))
(pow.f64 (.f64 (.f64 (PI.f64) (.f64 2 n)) (.f64 (PI.f64) (*.f64 2 n))) (+.f64 1/4 (/.f64 k -4)))
(pow.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) (.f64 n 4))) (+.f64 1/4 (/.f64 k -4)))
(.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (/.f64 k -2))) (pow.f64 2 (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(*.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (PI.f64) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/4 (/.f64 k -4)))) (pow.f64 n (+.f64 1/4 (/.f64 k -4))))
(.f64 (pow.f64 n (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (pow.f64 n (+.f64 1/4 (/.f64 k -4))) (pow.f64 n (+.f64 1/4 (/.f64 k -4)))))
(.f64 (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
(.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
(.f64 (/.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) 2) (.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2)))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 (.f64 (PI.f64) 4) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (/.f64 n 2) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 (/.f64 n 2) (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 (PI.f64) 4) (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 1)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(/.f64 (.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 2)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(/.f64 (.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) 4) 4)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(/.f64 (.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2)))) 4) 8)
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2)))
(fabs.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))))
(fabs.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2))))
(fabs.f64 (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (/.f64 k -2))))

localize68.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	0.2b	(pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
	0.2b	(.f64 (.f64 2 (PI.f64)) n)

Compiler

Compiled 50 to 34 computations (32% saved)

series27.0ms (0.1%)

Counts

1 → 12

Calls

6 calls:

Time	Variable		Point	Expression
25.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
1.0ms	k	@	0	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.0ms	k	@	inf	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.0ms	n	@	0	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

rewrite238.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1396×	`rational_best-4`
1396×	`rational_best-2`
1396×	`rational_best-3`
1396×	`rational_best-1`
1396×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	113	43
2	264	43
3	783	43
4	3343	43

Stop Event

1×	node limit

Counts

1 → 59

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Outputs
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Outputs

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simplify530.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1200×	`rational_best-simplify-47`
1194×	`rational_best-simplify-57`
966×	`rational_best-simplify-55`
820×	`rational_best-simplify-50`
616×	`rational_best-simplify-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	162	3517
1	393	3501
2	1259	3501
3	5663	3501

Stop Event

1×	node limit

Counts

71 → 73

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (sqrt.f64 k))))
(+.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) 4)) (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 3) (*.f64 (sqrt.f64 k) 4)))
(+.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) 4)))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 0)
(-.f64 0 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) -2)))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (sqrt.f64 k))) (+.f64 (/.f64 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) 2) 0))
(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 (sqrt.f64 k) 4)))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 3) (.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (*.f64 (sqrt.f64 k) 4)) 0))
(.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 2 (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 1 (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(.f64 1/2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2)))
(.f64 1/2 (-.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/4) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (-.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2)) 1/2)
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1/2 (.f64 2 (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (.f64 2 (sqrt.f64 k)))))
(.f64 1/4 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/4))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (-.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (-.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/4) 1/4)
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (/.f64 1/2 (*.f64 (sqrt.f64 k) 4)))
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (-.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (/.f64 1/2 (.f64 (sqrt.f64 k) 4))))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
(.f64 -2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) -2)))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 1 (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 2 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (.f64 2 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) 1/2))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) 1/2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (.f64 2 (sqrt.f64 k))))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(neg.f64 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))

Outputs
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) 1/2))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (.f64 1/2 (-.f64 1 k)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k)))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
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(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (.f64 1/2 (-.f64 1 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k)))))
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(+.f64 0 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
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(-.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 2 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) -2)))
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(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 1/2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 1/2 (-.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/4) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))) (-.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (/.f64 1/2 (.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1/2 (.f64 2 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 1/4 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/4))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (-.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (-.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (-.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/4) 1/4)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (/.f64 1/2 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (-.f64 (/.f64 1/2 (.f64 2 (sqrt.f64 k))) (/.f64 1/2 (.f64 (sqrt.f64 k) 4))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)))
(.f64 -2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) -2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) 4)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) 4)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (.f64 2 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) 1/2))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) 1/2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (.f64 2 (sqrt.f64 k))))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(neg.f64 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))

eval505.0ms (1.3%)

Compiler: Compiled 8175 to 5478 computations (33% saved)

prune324.0ms (0.8%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	336	17	353
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	336	19	355

Error

0.0b

Counts

355 → 19

Alt Table

Click to see full alt table

Status	Error	Program
	22.4b	(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) (.f64 n 4))) (+.f64 1/4 (/.f64 k -4))) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 1/2)))
	0.6b	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))
	5.5b	(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
	20.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
▶	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
▶	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
▶	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))) (sqrt.f64 k))
	21.4b	(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
▶	21.3b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
▶	3.2b	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
	0.5b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
	5.4b	(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))))
	21.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
	21.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))

Compiler

Compiled 738 to 582 computations (21.1% saved)

localize165.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 n (+.f64 1/2 (/.f64 k -2)))
✓	0.2b	(.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))) (sqrt.f64 k))
✓	0.2b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))

Compiler

Compiled 121 to 91 computations (24.8% saved)

series192.0ms (0.5%)

Counts

4 → 84

Calls

24 calls:

Time	Variable		Point	Expression
56.0ms	n	@	-inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
45.0ms	n	@	0	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
32.0ms	n	@	inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
19.0ms	k	@	-inf	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
19.0ms	k	@	inf	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))) (sqrt.f64 k))

rewrite536.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2034×	`rational_best-4`
2034×	`rational_best-2`
2034×	`rational_best-3`
2034×	`rational_best-1`
772×	`rational_best-simplify-50`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	246
1	163	246
2	383	210
3	1117	198
4	4880	198

Stop Event

1×	node limit

Counts

4 → 109

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4)))))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))
(pow.f64 n (+.f64 1/2 (/.f64 k -2)))

Outputs
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simplify624.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1260×	`rational_best-simplify-63`
946×	`rational_best-simplify-64`
808×	`rational_best-simplify-67`
664×	`rational_best-simplify-50`
606×	`rational_best-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	12825
1	1085	12639
2	3548	12459

Stop Event

1×	node limit

Counts

193 → 207

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 (.f64 n (PI.f64))))))))))
(+.f64 (.f64 (pow.f64 k 3) (+.f64 (.f64 -1/16 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (log.f64 n) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 3)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 n) (+.f64 (.f64 -1/64 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3)) (sqrt.f64 (PI.f64)))) (.f64 -1/192 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3)) (sqrt.f64 (PI.f64)))))) (.f64 -1/16 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 (.f64 n (PI.f64)))))))))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/4 (.f64 1/4 k))) 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/4 (.f64 1/4 k))) 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/4 (.f64 1/4 k))) 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/4 (.f64 1/4 k))) 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (pow.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 -1/4 k))) 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
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(.f64 (sqrt.f64 k) (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
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(.f64 (/.f64 (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) 4) (sqrt.f64 k)) (/.f64 1 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 k))))
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(+.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 0)
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(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) 2)
(/.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4)))) 4)
(/.f64 (+.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4)))) (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))) 8)
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(/.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 2 (.f64 2 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4)))))) 16)
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 1)
(+.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 0)
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(.f64 1/2 (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) 1)
(.f64 1 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 n 1/2) (pow.f64 n (.f64 k -1/2)))
(.f64 (pow.f64 n (.f64 k -1/2)) (pow.f64 n 1/2))
(.f64 (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 1/2)
(.f64 (.f64 (pow.f64 n 1/2) 2) (/.f64 (pow.f64 n (*.f64 k -1/2)) 2))
(.f64 (.f64 (pow.f64 n (*.f64 k -1/2)) 2) (/.f64 (pow.f64 n 1/2) 2))
(.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) 1/4)
(.f64 (pow.f64 n (.f64 k -1/4)) (.f64 (pow.f64 n (.f64 k -1/4)) (pow.f64 n 1/2)))
(.f64 (pow.f64 n (.f64 k -1/4)) (pow.f64 n (+.f64 (*.f64 k -1/4) 1/2)))
(.f64 (pow.f64 n (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/4 (*.f64 k -1/4))))
(.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 1/2 (+.f64 1/2 (*.f64 k -1/2))))
(/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 1)
(/.f64 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 2)
(/.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) 4)
(/.f64 (+.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))) 8)

Outputs
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))))
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(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4))) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) 4))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (*.f64 k -1/4)))) 4) (sqrt.f64 k)) 1/4)
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) 4) (sqrt.f64 k)) (/.f64 1 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 k))))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 2 (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) 4)) (/.f64 1 (.f64 2 (.f64 (sqrt.f64 k) 4))))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4))) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (*.f64 k -1/4))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4))) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (*.f64 k -1/4)))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (.f64 k -1/4)))) 4)) (/.f64 (/.f64 1 (*.f64 (sqrt.f64 k) 4)) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(pow.f64 (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 4 (.f64 (PI.f64) (PI.f64))) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k)) 1)
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (*.f64 k -1/4)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 (PI.f64) 4)) (+.f64 1/4 (.f64 k -1/4))) (/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(+.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 0)
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(+.f64 0 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(+.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 2) (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(-.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 0)
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 2) (/.f64 (neg.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) 2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 1)
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) 2)
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(/.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4)))) 4)
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 4)) 4)
(/.f64 (.f64 4 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (*.f64 k -1/4))))) 4)
(/.f64 (+.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4)))) (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))) 8)
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 4)) 4)
(/.f64 (.f64 4 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (*.f64 k -1/4))))) 4)
(/.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))) (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))) 16)
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 4)) 4)
(/.f64 (.f64 4 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (*.f64 k -1/4))))) 4)
(/.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 2 (.f64 2 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4)))))) 16)
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 4)) 4)
(/.f64 (.f64 4 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (*.f64 k -1/4))))) 4)
(pow.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 1)
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (.f64 k -1/4))))
(+.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 0)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(+.f64 0 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(+.f64 (/.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) 2))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(-.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 0)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(-.f64 (/.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 (neg.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 2))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 1/2 (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) 1)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 1 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (pow.f64 n 1/2) (pow.f64 n (.f64 k -1/2)))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (pow.f64 n (.f64 k -1/2)) (pow.f64 n 1/2))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 1/2)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (.f64 (pow.f64 n 1/2) 2) (/.f64 (pow.f64 n (*.f64 k -1/2)) 2))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (.f64 (pow.f64 n (*.f64 k -1/2)) 2) (/.f64 (pow.f64 n 1/2) 2))
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) 1/4)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(.f64 (pow.f64 n (.f64 k -1/4)) (.f64 (pow.f64 n (.f64 k -1/4)) (pow.f64 n 1/2)))
(.f64 (pow.f64 n (.f64 k -1/4)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/4))))
(.f64 (pow.f64 n 1/2) (pow.f64 (.f64 n n) (*.f64 k -1/4)))
(.f64 (pow.f64 n (.f64 k -1/4)) (pow.f64 n (+.f64 (*.f64 k -1/4) 1/2)))
(.f64 (pow.f64 n (.f64 k -1/4)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/4))))
(.f64 (pow.f64 n 1/2) (pow.f64 (.f64 n n) (*.f64 k -1/4)))
(.f64 (pow.f64 n (+.f64 1/4 (.f64 k -1/4))) (pow.f64 n (+.f64 1/4 (*.f64 k -1/4))))
(pow.f64 (.f64 n n) (+.f64 1/4 (.f64 k -1/4)))
(.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 1/2 (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 (+.f64 n n) 1/2) (+.f64 1/2 (.f64 k -1/2)))
(pow.f64 (.f64 1/2 (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))
(/.f64 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))) 1)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(/.f64 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 2)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(/.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) 4)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))
(/.f64 (+.f64 (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 2 (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))) 8)
(pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))

localize37.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (PI.f64) (.f64 n 2))
✓	0.3b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
✓	0.3b	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))

Compiler

Compiled 31 to 19 computations (38.7% saved)

series26.0ms (0.1%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
17.0ms	k	@	-inf	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
1.0ms	n	@	0	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
1.0ms	k	@	0	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
1.0ms	n	@	0	(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
1.0ms	n	@	-inf	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))

rewrite243.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

924×	`rational_best-simplify-64`
892×	`rational_best-4`
892×	`rational_best-2`
892×	`rational_best-3`
892×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	63
1	90	63
2	202	63
3	579	63
4	2249	63

Stop Event

1×	node limit

Counts

3 → 131

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(.f64 (PI.f64) (.f64 n 2))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) n) (neg.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) n) (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 8)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 2 (*.f64 n 8))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) 4) (*.f64 n 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (PI.f64) (*.f64 2 (*.f64 n 8))) (*.f64 (PI.f64) (*.f64 2 (*.f64 n 8)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))))

simplify286.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1150×	`rational_best-simplify-65`
1112×	`rational_best-simplify-1`
866×	`rational_best-simplify-63`
726×	`rational_best-simplify-67`
680×	`rational_best-simplify-47`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	3641
1	623	3635
2	2177	3631

Stop Event

1×	node limit

Counts

143 → 148

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -2)))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) 4))
(+.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) 4) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))
(+.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 2) (-.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) -2)))
(-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -2))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) 4) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 4))
(-.f64 (-.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -2)) (-.f64 0 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1/2)
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) -1)
(.f64 (.f64 2 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (+.f64 n n)) 2))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) 1/4)
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n))
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (.f64 2 (sqrt.f64 (+.f64 n n))) (/.f64 (sqrt.f64 (PI.f64)) 2))
(.f64 -2 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -2))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (.f64 2 (sqrt.f64 (+.f64 n n))))
(.f64 (/.f64 (sqrt.f64 (+.f64 n n)) 2) (.f64 2 (sqrt.f64 (PI.f64))))
(.f64 (sqrt.f64 1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 4))))
(.f64 (sqrt.f64 (.f64 n 4)) (sqrt.f64 (/.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (.f64 n 4)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 4))) (sqrt.f64 1/2))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)
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(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)) 8)
(/.f64 (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) 4) 16)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
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(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
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(+.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) -1) (neg.f64 (-.f64 1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) -1) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (-.f64 1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 k) 4))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) (-.f64 -1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))))) -1)
(+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)))
(+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))) (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 k) 4))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (-.f64 -1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))))) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) 1))
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k)))))
(-.f64 0 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k)))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)))
(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(-.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k)) (.f64 -2 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k)))))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) -4)))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) -4)) 0))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -4)) (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 (sqrt.f64 k) 4)) (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k)))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2))) (-.f64 0 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k)))
(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) 1) (-.f64 (-.f64 -1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (-.f64 1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))))) (-.f64 -1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 3) (.f64 (sqrt.f64 k) 4))) (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
(.f64 2 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 2 (sqrt.f64 k))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 1 (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(.f64 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (-.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 2 (sqrt.f64 k))) 2)
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) 1/2)
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1 (.f64 (sqrt.f64 k) 4))))
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))))
(.f64 1/2 (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (-.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k)))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (-.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4)) (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)))
(.f64 (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) (sqrt.f64 k)) 1/4)
(.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4)) (/.f64 1/2 (*.f64 (sqrt.f64 k) 4)))
(.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4)) (-.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (/.f64 1/2 (.f64 (sqrt.f64 k) 4))))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) -2) (-.f64 0 (/.f64 1/2 (sqrt.f64 k))))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(.f64 (/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(.f64 -2 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) -2)))
(.f64 1/4 (/.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) (.f64 2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)))
(.f64 (/.f64 1 (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k)))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 2 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -4) (-.f64 0 (/.f64 1 (.f64 (sqrt.f64 k) 4))))
(pow.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k)))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(-.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(-.f64 (.f64 (PI.f64) n) (neg.f64 (.f64 (PI.f64) n)))
(-.f64 (.f64 (PI.f64) n) (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(/.f64 (.f64 (PI.f64) (.f64 n 8)) 4)
(/.f64 (.f64 (PI.f64) (.f64 2 (*.f64 n 8))) 8)
(/.f64 (.f64 (.f64 (PI.f64) 4) (*.f64 n 8)) 16)
(/.f64 (+.f64 (.f64 (PI.f64) (.f64 2 (.f64 n 8))) (.f64 (PI.f64) (.f64 2 (.f64 n 8)))) 16)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
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(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
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(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
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(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
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(-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
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(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -2))
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(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
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(.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) -1)
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(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
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(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -4) (-.f64 0 (/.f64 1 (.f64 (sqrt.f64 k) 4))))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) -4) (neg.f64 (/.f64 1 (.f64 4 (sqrt.f64 k)))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 -4 (neg.f64 (/.f64 1/4 (sqrt.f64 k)))))
(pow.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(*.f64 (PI.f64) (+.f64 n n))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(*.f64 (PI.f64) (+.f64 n n))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(*.f64 (PI.f64) (+.f64 n n))
(-.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(*.f64 (PI.f64) (+.f64 n n))
(-.f64 (.f64 (PI.f64) n) (neg.f64 (.f64 (PI.f64) n)))
(*.f64 (PI.f64) (+.f64 n n))
(-.f64 (.f64 (PI.f64) n) (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2))
(*.f64 (PI.f64) (+.f64 n n))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(*.f64 (PI.f64) (+.f64 n n))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(/.f64 (.f64 (PI.f64) (.f64 n 8)) 4)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(/.f64 (.f64 (PI.f64) (.f64 2 (*.f64 n 8))) 8)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(/.f64 (.f64 (.f64 (PI.f64) 4) (*.f64 n 8)) 16)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(/.f64 (+.f64 (.f64 (PI.f64) (.f64 2 (.f64 n 8))) (.f64 (PI.f64) (.f64 2 (.f64 n 8)))) 16)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(*.f64 (PI.f64) (+.f64 n n))

localize126.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
	0.2b	(.f64 (PI.f64) (.f64 n 2))
✓	0.2b	(log.f64 (.f64 (PI.f64) (.f64 n 2)))
✓	3.2b	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2)))

Compiler

Compiled 73 to 52 computations (28.8% saved)

series9.0ms (0%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
1.0ms	n	@	0	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2)))
1.0ms	n	@	inf	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2)))
1.0ms	n	@	-inf	(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2)))
1.0ms	k	@	0	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))

rewrite325.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1264×	`rational_best-2`
1264×	`rational_best-1`
1262×	`rational_best-4`
1262×	`rational_best-3`
1262×	`exponential-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	111
1	126	111
2	252	107
3	774	95
4	3136	95

Stop Event

1×	node limit

Counts

3 → 123

Calls

Call 1

Inputs

(exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 (-.f64 1 k) 1/2)))

(log.f64 (*.f64 (PI.f64) (*.f64 n 2)))

(/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) (neg.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 3) 4) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 2) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 3) 4) (/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (PI.f64) 1/2) (-.f64 1 k)) (pow.f64 (+.f64 n n) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 n n) (*.f64 (-.f64 1 k) 1/2)) (pow.f64 (pow.f64 (PI.f64) 1/2) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 n (*.f64 (-.f64 1 k) 1/2)) (pow.f64 (*.f64 (PI.f64) 2) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) 2) (*.f64 (-.f64 1 k) 1/2)) (pow.f64 n (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 2 1/2) (-.f64 1 k)) (pow.f64 (*.f64 (PI.f64) n) (*.f64 (-.f64 1 k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 (-.f64 1 k) 1/2)) (pow.f64 (pow.f64 2 1/2) (-.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) (neg.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (/.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1 k)) 4)) (exp.f64 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 1 k)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) (-.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) (*.f64 (-.f64 1 k) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (-.f64 (*.f64 -2 k) -2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) 1/2) (-.f64 (*.f64 -2 k) -2))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (neg.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 2 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 2 (*.f64 2 (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))))

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simplify463.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1094×	`rational_best-simplify-1`
986×	`rational_best-simplify-67`
674×	`rational_best-simplify-63`
568×	`rational_best-simplify-47`
528×	`rational_best-simplify-80`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	7291
1	766	7171
2	2421	7123

Stop Event

1×	node limit

Counts

171 → 190

Calls

Call 1

Inputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
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(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) 4))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1/4) 1/4)
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (/.f64 1/2 (.f64 (sqrt.f64 k) 4)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(.f64 -2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) -2)))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 1 (/.f64 2 (sqrt.f64 k))) (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(neg.f64 (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))

Outputs
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 (-.f64 1 k) (.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64)))))))
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(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
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(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
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(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))))
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(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 2)) 1/8)) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) 3)))))))
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(+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 k (sqrt.f64 2)))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 2))) (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (*.f64 (PI.f64) n)))) 3))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(exp.f64 (.f64 1/2 (.f64 (+.f64 1 (.f64 -1 k)) (log.f64 (.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (.f64 1/2 (.f64 (-.f64 1 k) (log.f64 (.f64 2 (.f64 (PI.f64) n))))))
(exp.f64 (.f64 (log.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 1/2 (-.f64 1 k))))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
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(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
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(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (-.f64 1 k) 1/2)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) 4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 (+.f64 -1 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k)))) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (/.f64 (+.f64 -1 (.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))
(neg.f64 (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (-.f64 1 k) 1/2)) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 1/2 (-.f64 1 k))) (sqrt.f64 k))

localize307.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 n (+.f64 1/2 (/.f64 k -2)))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
✓	0.3b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
✓	0.6b	(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2)))

Compiler

Compiled 74 to 54 computations (27% saved)

series50.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
35.0ms	n	@	0	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
3.0ms	k	@	0	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
2.0ms	k	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
1.0ms	k	@	0	(.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
1.0ms	k	@	inf	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))

rewrite386.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1568×	`rational_best-2`
1568×	`rational_best-3`
1568×	`rational_best-1`
1566×	`rational_best-4`
1566×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	103
1	131	103
2	334	103
3	951	103
4	3846	103

Stop Event

1×	node limit

Counts

3 → 101

Calls

Call 1

Inputs

(pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2)))

(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))

(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 (neg.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/2) (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (pow.f64 (*.f64 2 (PI.f64)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 2 (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 1/2) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (pow.f64 2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (*.f64 k -1/2)) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/2) (pow.f64 (pow.f64 2 k) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/2) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (pow.f64 (PI.f64) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 2 k) -1/2) (*.f64 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 2 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/2) (pow.f64 (pow.f64 2 k) -1/2)) (pow.f64 (PI.f64) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (pow.f64 (PI.f64) 1/2)) (pow.f64 2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) (pow.f64 2 1/2)) (pow.f64 (PI.f64) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 2 1/2)) (pow.f64 (pow.f64 2 k) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2))) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (pow.f64 2 (+.f64 1/2 (*.f64 k -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) 1/2)) (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (*.f64 k -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 2 (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k -4)) (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k -4)) (pow.f64 (*.f64 2 (PI.f64)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (/.f64 k -4)) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 (/.f64 k -4) 1/4)) (pow.f64 (*.f64 2 (PI.f64)) (+.f64 (/.f64 k -4) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) 4) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 1/2 (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 2 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2)))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 4) (/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 3) 4) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 3) 4) (/.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 2 (*.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 2 (*.f64 2 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (*.f64 k -1/2)))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (+.f64 1/2 (neg.f64 k)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (*.f64 2 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (*.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (*.f64 2 (sqrt.f64 k))) 2) (/.f64 (*.f64 3/2 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (*.f64 (sqrt.f64 k) 4)) (/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 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#<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))))))

simplify551.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1036×	`rational_best-simplify-63`
892×	`rational_best-simplify-67`
608×	`rational_best-simplify-50`
588×	`rational_best-simplify-64`
572×	`rational_best-simplify-47`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	339	7225
1	898	7087
2	2795	6943

Stop Event

1×	node limit

Counts

149 → 168

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (+.f64 (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64)))))))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 (.f64 n (PI.f64))))))))))
(+.f64 (.f64 (+.f64 (.f64 -1/16 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (log.f64 n) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 3)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1/16 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3)) (sqrt.f64 (.f64 n (PI.f64)))))))) (pow.f64 k 3)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 (.f64 n (PI.f64)))))))))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
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(.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) 4)) (/.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) 2) (sqrt.f64 k)))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(neg.f64 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))

Outputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))
(sqrt.f64 (*.f64 2 (PI.f64)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))))
(+.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 k (sqrt.f64 2))) -1/2)))
(+.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64))))))
(.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 (sqrt.f64 2) k)))))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (PI.f64))))) (sqrt.f64 (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (PI.f64))) 2))) (sqrt.f64 (PI.f64))))))
(+.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) 2)) 1/8)) (+.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (*.f64 k (sqrt.f64 2))) -1/2))))
(+.f64 (sqrt.f64 (.f64 2 (PI.f64))) (+.f64 (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 2 (PI.f64))))) (.f64 1/8 (.f64 (pow.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) 2) (sqrt.f64 (*.f64 2 (PI.f64)))))))
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(+.f64 (+.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) 2)) 1/8)) (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) 3)) -1/48))) (+.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 (sqrt.f64 (PI.f64)) (.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 k (sqrt.f64 2))) -1/2))))
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(+.f64 (.f64 (sqrt.f64 (PI.f64)) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 (sqrt.f64 2) k))))) (.f64 (sqrt.f64 (PI.f64)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) 2))) (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (PI.f64)))) 3))))))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 k 1/2)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
(sqrt.f64 (.f64 (PI.f64) (.f64 n 2)))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))))
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(+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 (.f64 k (.f64 -1/2 (+.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))) (.f64 (log.f64 n) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))))) (.f64 (pow.f64 k 2) (+.f64 (.f64 1/8 (.f64 (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (+.f64 (.f64 1/4 (.f64 (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 1/8 (.f64 (pow.f64 (log.f64 n) 2) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))))))
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(+.f64 (.f64 (+.f64 (.f64 -1/16 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (log.f64 n) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 3)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 -1/16 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3)) (sqrt.f64 (.f64 n (PI.f64)))))))) (pow.f64 k 3)) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 k (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) (sqrt.f64 (.f64 n (PI.f64))))))) (.f64 (pow.f64 k 2) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 1/4 (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 2)) (sqrt.f64 (.f64 n (PI.f64)))))))))))
(+.f64 (+.f64 (.f64 k (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (log.f64 (.f64 2 (PI.f64)))))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (log.f64 n)) -1/2)))) (.f64 (pow.f64 k 2) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2)))) (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))) 1/4)) (.f64 1/8 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 2)))))))) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (pow.f64 k 3) (+.f64 (+.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (log.f64 n) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 2))) -1/16)) (.f64 -1/48 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 (.f64 2 (PI.f64))) 3))))) (+.f64 (.f64 -1/48 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 n) 3)))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (.f64 (log.f64 (.f64 2 (PI.f64))) (pow.f64 (log.f64 n) 2))) -1/16)))))))
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(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 k 1/2)))
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(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (-.f64 1/2 (.f64 1/2 k))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (-.f64 1/2 (*.f64 k 1/2)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (-.f64 1/2 (*.f64 k 1/2)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
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(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
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(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
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(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (.f64 -1/2 k))))
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(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (*.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 1/2 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 -2 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) -2) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 4) (/.f64 (/.f64 1/2 (sqrt.f64 k)) 2))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) 2) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 4))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) 4) (sqrt.f64 k)) 1/4)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) 4)) (/.f64 1 (.f64 2 (.f64 (sqrt.f64 k) 4))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 k -1/2))) 4)) (/.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) 2) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (+.f64 -1 (*.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (sqrt.f64 k)))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k)) (+.f64 -1 (*.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(pow.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(neg.f64 (neg.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 k))

localize256.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
✓	0.2b	(*.f64 (PI.f64) n)
✓	0.3b	(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)

Compiler

Compiled 74 to 42 computations (43.2% saved)

series76.0ms (0.2%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
35.0ms	k	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
19.0ms	n	@	0	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
5.0ms	n	@	inf	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
3.0ms	k	@	0	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
2.0ms	n	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))

rewrite562.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1450×	`rational_best-4`
1450×	`rational_best-2`
1450×	`rational_best-3`
1450×	`rational_best-1`
1450×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	146
1	128	146
2	304	146
3	882	146
4	3528	146

Stop Event

1×	node limit

Counts

4 → 95

Calls

Call 1

Inputs
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)
(*.f64 (PI.f64) n)
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) 2) (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) 2) (/.f64 (neg.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 1/2) (pow.f64 (.f64 (PI.f64) n) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) n) 1/2) (pow.f64 2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (PI.f64) 1/2) (pow.f64 (+.f64 n n) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 n 1/2) (pow.f64 (.f64 2 (PI.f64)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 2 (PI.f64)) 1/2) (pow.f64 n 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 (.f64 (PI.f64) n) 1/2)) (/.f64 (pow.f64 2 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 2 1/2)) (/.f64 (pow.f64 (.f64 (PI.f64) n) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 n n) 1/2) (pow.f64 (PI.f64) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (PI.f64) (.f64 n 4)) 1/2) (pow.f64 1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2))) (.f64 2 (.f64 2 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)))) 8)))))
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simplify467.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1094×	`rational_best-simplify-1`
904×	`rational_best-simplify-67`
878×	`rational_best-simplify-63`
552×	`rational_best-simplify-64`
470×	`rational_best-simplify-47`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	5233
1	603	5177
2	2119	5137

Stop Event

1×	node limit

Counts

119 → 125

Calls

Call 1

Inputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
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(/.f64 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 k -1/2))) 4) 4)
(/.f64 (.f64 2 (.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2))) 4)) 8)
(/.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2))) (.f64 2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2))))) 16)
(/.f64 (.f64 (.f64 2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)))) (.f64 2 (.f64 2 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)))) 16)
(pow.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2))) 1)
(neg.f64 (neg.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)))))

Outputs
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
(*.f64 n (PI.f64))
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(*.f64 n (PI.f64))
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(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 (PI.f64) 2)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
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(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/2) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)))
(pow.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2))) 1)
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/2) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)))
(neg.f64 (neg.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 k -1/2)))))
(.f64 (pow.f64 (.f64 n (.f64 (PI.f64) 2)) 1/2) (pow.f64 (.f64 n (.f64 (PI.f64) 2)) (.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)))

eval2.5s (6.5%)

Compiler: Compiled 26916 to 16576 computations (38.4% saved)

prune821.0ms (2.1%)

Pruning

21 alts after pruning (17 fresh and 4 done)

	Pruned	Kept	Total
New	905	12	917
Fresh	7	5	12
Picked	1	0	1
Done	2	4	6
Total	915	21	936

Error

Counts

936 → 21

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 1/2)))
	0.6b	(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))
▶	20.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
	0.7b	(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (.f64 (pow.f64 (+.f64 n n) 1/2) (pow.f64 (PI.f64) 1/2))) (sqrt.f64 k))
✓	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
	2.0b	(/.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
	21.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2)) (sqrt.f64 k))
	21.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n)) (sqrt.f64 k))
▶	2.0b	(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
✓	21.3b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
✓	3.2b	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (sqrt.f64 k)))
	0.6b	(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 (+.f64 1/4 (.f64 k -1/4)) 2)) (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k))))
	26.6b	(.f64 (/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
	26.3b	(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))))
	21.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
▶	21.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
▶	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))

Compiler

Compiled 721 to 557 computations (22.7% saved)

localize71.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
	0.2b	(.f64 (PI.f64) (.f64 n 2))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))

Compiler

Compiled 59 to 43 computations (27.1% saved)

series33.0ms (0.1%)

Counts

3 → 36

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	k	@	-inf	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
1.0ms	k	@	0	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
1.0ms	n	@	-inf	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
1.0ms	n	@	inf	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
1.0ms	n	@	0	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))

rewrite328.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1522×	`rational_best-simplify-63`
1196×	`rational_best-4`
1196×	`rational_best-2`
1196×	`rational_best-3`
1196×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	93
1	133	93
2	292	93
3	853	93
4	2983	93

Stop Event

1×	node limit

Counts

3 → 84

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
(pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(sqrt.f64 (/.f64 1 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 4) (+.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 4) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2) (+.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) -2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 4) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4) (*.f64 (sqrt.f64 (/.f64 1 k)) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4) (+.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2) (/.f64 (pow.f64 (*.f64 (PI.f64) 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (*.f64 k -1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (*.f64 k -1/2)) (*.f64 (pow.f64 2 1/2) (pow.f64 (*.f64 (PI.f64) n) (+.f64 1/2 (*.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (*.f64 k -1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 (*.f64 (PI.f64) n) (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) n) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 2 (+.f64 1/2 (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/2) (*.f64 (pow.f64 (*.f64 (PI.f64) n) 1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 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n)) (*.f64 k -1/2)) (pow.f64 2 1/2)) (pow.f64 (*.f64 (PI.f64) n) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))) (pow.f64 (+.f64 n n) 1/2)) (pow.f64 (+.f64 n n) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (pow.f64 (PI.f64) 1/2)) (pow.f64 (+.f64 n n) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (+.f64 n n) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (/.f64 1 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (/.f64 (sqrt.f64 (/.f64 1 k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 4) (+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 4) (/.f64 (sqrt.f64 (/.f64 1 k)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (/.f64 1 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (/.f64 (sqrt.f64 (/.f64 1 k)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) -2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (sqrt.f64 (/.f64 1/4 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1/4 k)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 1 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 4) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1 k)) 1)))))

simplify402.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1258×	`rational_best-simplify-52`
1204×	`rational_best-simplify-48`
1116×	`rational_best-simplify-1`
684×	`rational_best-simplify-51`
624×	`rational_best-simplify-63`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	5366
1	582	5232
2	1600	5188
3	5170	5188

Stop Event

1×	node limit

Counts

120 → 151

Calls

Call 1

Inputs
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 3) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (-.f64 1/2 (*.f64 1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 2 (.f64 n (PI.f64))) (+.f64 1/2 (*.f64 -1/2 k)))
(+.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 0)
(+.f64 0 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))))
(+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 2))
(+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 4) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 4) (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2)))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 0)
(-.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) -2))
(-.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 2) (+.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) -2) 0))
(/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 1)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))) 2)
(/.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4)) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 1 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4))) 8)
(/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 4) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4)) 16)
(/.f64 (.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (*.f64 (sqrt.f64 (/.f64 1 k)) 4)) 16)
(pow.f64 (.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 1)
(+.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0)
(+.f64 0 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2)))
(-.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 0)
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) -2))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) -2) 0))
(.f64 1 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 1/2 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 1)
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2))
(.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (+.f64 n n) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (PI.f64) (+.f64 1/2 (*.f64 k -1/2))))
(.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) 1/2)
(.f64 (pow.f64 (PI.f64) 1/2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (+.f64 n n) 1/2)))
(.f64 (pow.f64 (PI.f64) (.f64 k -1/2)) (.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (PI.f64) 1/2)))
(.f64 (pow.f64 (+.f64 n n) 1/2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (PI.f64) 1/2)))
(.f64 (pow.f64 (+.f64 n n) (.f64 k -1/2)) (.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (+.f64 n n) 1/2)))
(.f64 (pow.f64 2 (.f64 k -1/2)) (.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2)))
(.f64 (pow.f64 2 (.f64 k -1/2)) (.f64 (pow.f64 2 1/2) (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 2 (.f64 k -1/2))))
(.f64 (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 2 (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 2 1/2) (.f64 (pow.f64 (.f64 (PI.f64) n) 1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2))))
(.f64 (pow.f64 2 1/2) (.f64 (pow.f64 2 (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (*.f64 k -1/2)))))
(.f64 (pow.f64 (.f64 (PI.f64) n) 1/2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (pow.f64 2 1/2)))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (PI.f64) 1/2)) (pow.f64 (PI.f64) (.f64 k -1/2)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (+.f64 n n) 1/2)) (pow.f64 (PI.f64) 1/2))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 2 1/2)) (pow.f64 (*.f64 (PI.f64) n) 1/2))
(.f64 (.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (+.f64 n n) 1/2)) (pow.f64 (+.f64 n n) (.f64 k -1/2)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (PI.f64) 1/2)) (pow.f64 (+.f64 n n) 1/2))
(.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) 2))
(.f64 (.f64 2 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) 2))
(.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) 2))
(.f64 (.f64 2 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) 2))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) 1/4)
(.f64 (pow.f64 (.f64 (PI.f64) 2) (.f64 k -1/2)) (.f64 (pow.f64 n (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) 2) 1/2) (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (/.f64 k -4) 1/4)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 (/.f64 k -4) 1/4)))
(.f64 (pow.f64 (.f64 n 4) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (/.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 4)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 1/2 (+.f64 1/2 (*.f64 k -1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 1)
(/.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2)
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4) 4)
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4)) 8)
(fabs.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
(+.f64 (sqrt.f64 (/.f64 1 k)) 0)
(+.f64 0 (sqrt.f64 (/.f64 1 k)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (/.f64 (sqrt.f64 (/.f64 1 k)) 2))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 4) (+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 4) (/.f64 (sqrt.f64 (/.f64 1 k)) 2)))
(-.f64 (sqrt.f64 (/.f64 1 k)) 0)
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (/.f64 (sqrt.f64 (/.f64 1 k)) -2))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) -2) 0))
(*.f64 1 (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) 1)
(*.f64 2 (sqrt.f64 (/.f64 1/4 k)))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1/4 k)) 4))
(.f64 (.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 1/2)
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 4) 1/4)
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 k)))
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 1/2))
(/.f64 (sqrt.f64 (/.f64 1 k)) 1)
(/.f64 (*.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 2)
(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 4) 4)
(/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 4) 8)
(pow.f64 (sqrt.f64 (/.f64 1 k)) 1)

Outputs
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (sqrt.f64 (/.f64 1 k)))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k)))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (.f64 2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (log.f64 (.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 -2 (PI.f64))))))
(exp.f64 (.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (.f64 -1/2 k))))
(exp.f64 (.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (.f64 (PI.f64) -2))) (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 -1/2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) (sqrt.f64 (.f64 2 (*.f64 (PI.f64) n))))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (*.f64 (PI.f64) n))))))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (log.f64 (.f64 (PI.f64) (.f64 2 n))) (*.f64 k (sqrt.f64 2))))))
(+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64)))))) (sqrt.f64 (.f64 n (PI.f64))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 (.f64 2 (.f64 n (PI.f64)))) 2))) (sqrt.f64 (.f64 n (PI.f64)))))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n))))))) (+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (.f64 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 2)) 1/8))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (+.f64 (.f64 1/8 (.f64 (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 2) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))))) (.f64 -1/2 (.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) (sqrt.f64 (.f64 2 (.f64 (PI.f64) n)))))))
(+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) n))) (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (+.f64 (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))) 2))) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 (.f64 2 (.f64 (PI.f64) n)))))))))
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(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) 1/2))
(.f64 (pow.f64 2 1/2) (.f64 (pow.f64 2 (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) n) (+.f64 1/2 (*.f64 k -1/2)))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) n) 1/2) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (pow.f64 2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (.f64 (pow.f64 (*.f64 (PI.f64) n) 1/2) (pow.f64 2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) 1/2))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (PI.f64) 1/2)) (pow.f64 (PI.f64) (.f64 k -1/2)))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 2 (.f64 k -1/2))) (pow.f64 (.f64 (PI.f64) n) (.f64 k -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (.f64 (pow.f64 (.f64 (PI.f64) n) (*.f64 -1/2 k)) (pow.f64 (pow.f64 2 k) -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 -1/2 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (+.f64 n n) 1/2)) (pow.f64 (PI.f64) 1/2))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 2 1/2)) (pow.f64 (*.f64 (PI.f64) n) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (.f64 (pow.f64 (*.f64 (PI.f64) n) 1/2) (pow.f64 2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) 1/2))
(.f64 (.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (+.f64 n n) 1/2)) (pow.f64 (+.f64 n n) (.f64 k -1/2)))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (PI.f64) 1/2)) (pow.f64 (+.f64 n n) 1/2))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/2) 2))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 2 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2))) 2))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) 2))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 2 (pow.f64 (PI.f64) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (pow.f64 (+.f64 n n) (+.f64 1/2 (.f64 k -1/2))) 2))
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) 1/4)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (.f64 k -1/2)) (.f64 (pow.f64 n (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (.f64 (pow.f64 (.f64 (PI.f64) n) (*.f64 -1/2 k)) (pow.f64 (pow.f64 2 k) -1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (*.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (pow.f64 (.f64 (PI.f64) (.f64 2 n)) (*.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))
(pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (.f64 2 n)) (+.f64 1/2 (*.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) 2) 1/2) (.f64 (pow.f64 n 1/2) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2))))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (.f64 (pow.f64 (*.f64 (PI.f64) n) 1/2) (pow.f64 2 1/2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (pow.f64 (.f64 (PI.f64) (*.f64 2 n)) 1/2))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 (/.f64 k -4) 1/4)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (+.f64 (/.f64 k -4) 1/4)))
(pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (*.f64 (PI.f64) (+.f64 n n))) (+.f64 1/4 (/.f64 k -4)))
(pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (*.f64 (PI.f64) (+.f64 n n)))) (+.f64 1/4 (/.f64 k -4)))
(.f64 (pow.f64 (.f64 n 4) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 (/.f64 (PI.f64) 2) (+.f64 1/2 (.f64 k -1/2))))
(pow.f64 (.f64 (.f64 n 4) (/.f64 (PI.f64) 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 (PI.f64) (/.f64 (.f64 n 4) 2)) (+.f64 1/2 (*.f64 -1/2 k)))
(pow.f64 (.f64 n (+.f64 (PI.f64) (PI.f64))) (+.f64 1/2 (.f64 -1/2 k)))
(.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 4)) (+.f64 1/2 (.f64 k -1/2))) (pow.f64 1/2 (+.f64 1/2 (*.f64 k -1/2))))
(pow.f64 (.f64 (.f64 (PI.f64) (.f64 n 4)) 1/2) (+.f64 1/2 (.f64 -1/2 k)))
(pow.f64 (.f64 1/2 (.f64 (PI.f64) (.f64 n 4))) (+.f64 1/2 (.f64 -1/2 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 1)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(/.f64 (.f64 2 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2)))) 2)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4) 4)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4)) 8)
(pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k)))
(fabs.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))))
(fabs.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))))
(+.f64 (sqrt.f64 (/.f64 1 k)) 0)
(sqrt.f64 (/.f64 1 k))
(+.f64 0 (sqrt.f64 (/.f64 1 k)))
(sqrt.f64 (/.f64 1 k))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (/.f64 (sqrt.f64 (/.f64 1 k)) 2))
(sqrt.f64 (/.f64 1 k))
(+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 4) (+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 4) (/.f64 (sqrt.f64 (/.f64 1 k)) 2)))
(sqrt.f64 (/.f64 1 k))
(-.f64 (sqrt.f64 (/.f64 1 k)) 0)
(sqrt.f64 (/.f64 1 k))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (/.f64 (sqrt.f64 (/.f64 1 k)) -2))
(-.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (/.f64 1 k)) -2))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (+.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) -2) 0))
(-.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) 2) (/.f64 (sqrt.f64 (/.f64 1 k)) -2))
(-.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (/.f64 1 k)) -2))
(*.f64 1 (sqrt.f64 (/.f64 1 k)))
(sqrt.f64 (/.f64 1 k))
(*.f64 (sqrt.f64 (/.f64 1 k)) 1)
(sqrt.f64 (/.f64 1 k))
(*.f64 2 (sqrt.f64 (/.f64 1/4 k)))
(.f64 1/2 (.f64 (sqrt.f64 (/.f64 1/4 k)) 4))
(*.f64 2 (sqrt.f64 (/.f64 1/4 k)))
(.f64 (.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 1/2)
(*.f64 2 (sqrt.f64 (/.f64 1/4 k)))
(.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 4) 1/4)
(sqrt.f64 (/.f64 1 k))
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1/2 k)))
(sqrt.f64 (/.f64 1 k))
(*.f64 (sqrt.f64 (/.f64 2 k)) (sqrt.f64 1/2))
(sqrt.f64 (/.f64 1 k))
(/.f64 (sqrt.f64 (/.f64 1 k)) 1)
(sqrt.f64 (/.f64 1 k))
(/.f64 (*.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 2)
(/.f64 (*.f64 4 (sqrt.f64 (/.f64 1/4 k))) 2)
(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 4) 4)
(sqrt.f64 (/.f64 1 k))
(/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1/4 k)) 4) 4) 8)
(/.f64 (.f64 4 (.f64 4 (sqrt.f64 (/.f64 1/4 k)))) 8)
(/.f64 (*.f64 (sqrt.f64 (/.f64 1/4 k)) 16) 8)
(/.f64 (*.f64 16 (sqrt.f64 (/.f64 1/4 k))) 8)
(pow.f64 (sqrt.f64 (/.f64 1 k)) 1)
(sqrt.f64 (/.f64 1 k))

localize66.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (PI.f64) (+.f64 n n))
	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))

Compiler

Compiled 37 to 13 computations (64.9% saved)

series5.0ms (0%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	n	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
1.0ms	k	@	-inf	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
1.0ms	k	@	0	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
1.0ms	n	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
0.0ms	k	@	inf	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))

rewrite294.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

814×	`rational_best-simplify-63`
702×	`rational_best-2`
702×	`rational_best-3`
702×	`rational_best-1`
696×	`rational_best-4`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	69
1	94	63
2	188	63
3	512	63
4	1932	63

Stop Event

1×	node limit

Counts

3 → 193

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(*.f64 (PI.f64) (+.f64 n n))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 2)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (+.f64 (/.f64 0 (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (+.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (+.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))))) 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simplify624.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1324×	`rational_best-simplify-108`
1148×	`rational_best-simplify-55`
880×	`rational_best-simplify-65`
732×	`rational_best-simplify-50`
704×	`rational_best-simplify-64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	441	6487
1	1599	6331
2	7685	6325

Stop Event

1×	node limit

Counts

205 → 236

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
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(/.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 4)) (/.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 4)))
(/.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)) (sqrt.f64 k)) (/.f64 (/.f64 2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)) (.f64 (sqrt.f64 k) 2)) (/.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)) (.f64 (sqrt.f64 k) 4)) (/.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 4)))
(/.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 (/.f64 4 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 2)) (/.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (sqrt.f64 k) 2)))
(/.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k)) (.f64 (sqrt.f64 k) 4)) (/.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (sqrt.f64 k) 4)))
(pow.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
(+.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))
(-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (+.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2) 0))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (-.f64 0 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)))
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)
(.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 (sqrt.f64 (PI.f64)) 2)))
(.f64 2 (.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (+.f64 n n)) 2)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) 1/2)
(.f64 1/2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (.f64 2 (sqrt.f64 (+.f64 n n))))
(.f64 (.f64 2 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (+.f64 n n)) 2))
(.f64 (.f64 2 (sqrt.f64 (PI.f64))) (*.f64 1 (/.f64 (sqrt.f64 (+.f64 n n)) 2)))
(.f64 (.f64 2 (sqrt.f64 (+.f64 n n))) (/.f64 (sqrt.f64 (PI.f64)) 2))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) 1/4)
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))
(.f64 (/.f64 (sqrt.f64 (+.f64 n n)) 2) (.f64 2 (sqrt.f64 (PI.f64))))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) 2) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 (+.f64 n n)) 2)))
(.f64 (.f64 2 (.f64 2 (sqrt.f64 (PI.f64)))) (.f64 1/2 (/.f64 (sqrt.f64 (+.f64 n n)) 2)))
(.f64 (.f64 2 (.f64 2 (sqrt.f64 (+.f64 n n)))) (.f64 1/2 (/.f64 (sqrt.f64 (PI.f64)) 2)))
(.f64 (sqrt.f64 1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 4))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 (sqrt.f64 (.f64 n 4)) (sqrt.f64 (/.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))
(.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (.f64 n 4)))
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 4))) (sqrt.f64 1/2))
(.f64 (+.f64 (sqrt.f64 n) (sqrt.f64 n)) (.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (PI.f64)) 2)))
(.f64 (+.f64 (sqrt.f64 2) (sqrt.f64 2)) (.f64 (sqrt.f64 n) (/.f64 (sqrt.f64 (PI.f64)) 2)))
(.f64 (+.f64 (sqrt.f64 (.f64 n 4)) (sqrt.f64 (.f64 n 4))) (.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 (PI.f64)) 2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) 4)
(/.f64 (.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) 4) 8)
(/.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 4) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 4)) 16)
(/.f64 (.f64 (.f64 2 (.f64 2 (sqrt.f64 (PI.f64)))) (.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n))))) 16)
(/.f64 (.f64 (.f64 2 (.f64 2 (sqrt.f64 (+.f64 n n)))) (.f64 2 (*.f64 2 (sqrt.f64 (PI.f64))))) 16)
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(+.f64 (.f64 (PI.f64) (/.f64 n 2)) (+.f64 (.f64 (PI.f64) (/.f64 n 2)) (*.f64 (PI.f64) n)))
(-.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(-.f64 (.f64 (PI.f64) n) (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2))
(-.f64 (.f64 (PI.f64) n) (+.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2) 0))
(-.f64 (+.f64 (.f64 (PI.f64) (/.f64 n 2)) (.f64 (PI.f64) n)) (-.f64 0 (*.f64 (PI.f64) (/.f64 n 2))))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(/.f64 (.f64 n (.f64 2 (*.f64 (PI.f64) 4))) 4)
(/.f64 (.f64 (.f64 (.f64 n 4) 4) (.f64 (PI.f64) 2)) 16)
(/.f64 (.f64 (PI.f64) (.f64 (*.f64 n 4) 4)) 8)
(/.f64 (+.f64 (.f64 (PI.f64) (.f64 (.f64 n 4) 4)) (.f64 (PI.f64) (.f64 (.f64 n 4) 4))) 16)
(/.f64 (+.f64 (.f64 (.f64 (.f64 n 4) 4) (.f64 (PI.f64) 2)) (.f64 (.f64 (.f64 n 4) 4) (.f64 (PI.f64) 2))) 32)
(/.f64 (.f64 (.f64 2 (.f64 (PI.f64) 4)) (.f64 (*.f64 n 4) 4)) 64)
(/.f64 (.f64 (.f64 (.f64 n 4) 4) (.f64 2 (*.f64 (PI.f64) 4))) 64)
(/.f64 (.f64 (.f64 n 4) (.f64 2 (.f64 (PI.f64) 4))) 16)
(/.f64 (.f64 (.f64 (PI.f64) 2) (.f64 (.f64 n 4) 4)) 16)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)

Outputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 0 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
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(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (+.f64 (/.f64 0 (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (+.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) 0))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
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(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
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(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)))
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(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) (+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2))))
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(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -4))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2))) (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
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(-.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2))) (-.f64 0 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))) (neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
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(-.f64 (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2))) (-.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4))))
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(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -4)))
(-.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -4))) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) -2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
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(/.f64 (.f64 (.f64 2 (.f64 (PI.f64) 4)) (.f64 4 (*.f64 n 4))) 64)
(/.f64 (.f64 (.f64 (PI.f64) 8) (*.f64 n 16)) 64)
(/.f64 (.f64 (.f64 (.f64 n 4) 4) (.f64 2 (*.f64 (PI.f64) 4))) 64)
(/.f64 (.f64 (.f64 2 (.f64 (PI.f64) 4)) (.f64 4 (*.f64 n 4))) 64)
(/.f64 (.f64 (.f64 (PI.f64) 8) (*.f64 n 16)) 64)
(/.f64 (.f64 (.f64 n 4) (.f64 2 (.f64 (PI.f64) 4))) 16)
(/.f64 (.f64 4 (.f64 (.f64 n 4) (.f64 2 (PI.f64)))) 16)
(/.f64 (.f64 (PI.f64) (.f64 n 16)) 8)
(/.f64 (.f64 (.f64 (PI.f64) 2) (.f64 (.f64 n 4) 4)) 16)
(/.f64 (.f64 4 (.f64 (.f64 n 4) (.f64 2 (PI.f64)))) 16)
(/.f64 (.f64 (PI.f64) (.f64 n 16)) 8)
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(*.f64 (PI.f64) (+.f64 n n))

localize80.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 n (+.f64 1/2 (/.f64 k -2)))
✓	0.2b	(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
✓	0.4b	(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
✓	1.0b	(sqrt.f64 (*.f64 2 (PI.f64)))

Compiler

Compiled 59 to 42 computations (28.8% saved)

series40.0ms (0.1%)

Counts

3 → 36

Calls

12 calls:

Time	Variable		Point	Expression
14.0ms	k	@	0	(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
13.0ms	k	@	0	(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
2.0ms	k	@	-inf	(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
2.0ms	k	@	inf	(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
1.0ms	n	@	0	(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))

rewrite307.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1192×	`rational_best-4`
1192×	`rational_best-2`
1192×	`rational_best-3`
1192×	`rational_best-1`
1192×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	97
1	126	97
2	282	97
3	778	97
4	3017	97

Stop Event

1×	node limit

Counts

3 → 107

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 2 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 2) (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 2) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 3) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 3) 4) (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 2) (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 3) 4) (/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (*.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 2 (*.f64 2 (sqrt.f64 (*.f64 2 (PI.f64)))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 2 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)) (neg.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 (sqrt.f64 k) 4)) (/.f64 (*.f64 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simplify396.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1232×	`rational_best-simplify-1`
1022×	`rational_best-simplify-65`
896×	`rational_best-simplify-63`
694×	`rational_best-simplify-67`
648×	`rational_best-simplify-80`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	6283
1	658	6075
2	2201	6035

Stop Event

1×	node limit

Counts

143 → 142

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
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(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (/.f64 (PI.f64) k)))
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(+.f64 (sqrt.f64 (*.f64 2 (PI.f64))) 0)
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(-.f64 (sqrt.f64 (*.f64 2 (PI.f64))) 0)
(-.f64 (/.f64 (sqrt.f64 (.f64 2 (PI.f64))) 2) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (PI.f64)))) 2))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) 1)
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 2 (PI.f64)))))
(.f64 1 (sqrt.f64 (.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64)))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2))
(.f64 (.f64 2 (sqrt.f64 (*.f64 2 (PI.f64)))) 1/2)
(.f64 (/.f64 (sqrt.f64 2) 2) (.f64 2 (sqrt.f64 (PI.f64))))
(.f64 (.f64 2 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 2) 2))
(.f64 (.f64 2 (sqrt.f64 2)) (/.f64 (sqrt.f64 (PI.f64)) 2))
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Outputs
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(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))))
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(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
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(.f64 1/2 (-.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)) 1/4) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 -2 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 -2 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 1 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) (-.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4) (-.f64 (/.f64 1/2 (sqrt.f64 k)) (/.f64 1 (.f64 (sqrt.f64 k) 4))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (-.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (-.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (-.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)) 1/4) 1/4)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (/.f64 1/2 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (-.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (/.f64 1/2 (.f64 (sqrt.f64 k) 4))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 1/4 (/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)) 1/4))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (/.f64 (/.f64 1 (*.f64 (sqrt.f64 k) 4)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(pow.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(neg.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))

localize132.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
✓	0.2b	(.f64 (PI.f64) (.f64 n 4))
✓	0.3b	(pow.f64 (.f64 (PI.f64) (.f64 n 4)) (+.f64 1/2 (/.f64 k -2)))
✓	0.8b	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))

Compiler

Compiled 85 to 63 computations (25.9% saved)

series366.0ms (0.9%)

Counts

4 → 72

Calls

21 calls:

Time	Variable		Point	Expression
123.0ms	k	@	inf	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
111.0ms	n	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))
55.0ms	n	@	-inf	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))
26.0ms	n	@	inf	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))
23.0ms	k	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))

rewrite369.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1990×	`rational_best-4`
1990×	`rational_best-2`
1990×	`rational_best-3`
1990×	`rational_best-1`
1990×	`exponential-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	136
1	140	136
2	367	124
3	1121	124
4	4752	124

Stop Event

1×	node limit

Counts

4 → 139

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2))))
(pow.f64 (.f64 (PI.f64) (.f64 n 4)) (+.f64 1/2 (/.f64 k -2)))
(.f64 (PI.f64) (.f64 n 4))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (.f64 n 4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (PI.f64) (.f64 n 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (.f64 n 4)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 (.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (PI.f64) (+.f64 n n)) (/.f64 (neg.f64 (.f64 (PI.f64) (.f64 n 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (PI.f64) (.f64 n 8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) 8) (.f64 (.f64 (PI.f64) (+.f64 n n)) 8)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (PI.f64) 4) (.f64 2 (.f64 n 8))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 2 (.f64 n 8)) (.f64 (PI.f64) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 n 4) (.f64 (PI.f64) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (PI.f64) (.f64 n 4)) 1)))))
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simplify419.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1348×	`rational_best-simplify-63`
1076×	`rational_best-simplify-64`
798×	`rational_best-simplify-67`
656×	`rational_best-simplify-50`
622×	`rational_best-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	434	10097
1	1132	9795
2	3687	9625

Stop Event

1×	node limit

Counts

211 → 227

Calls

Call 1

Inputs
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 -4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 -1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 -4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 -1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 -4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 -1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 -4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 -1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
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(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
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(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(-.f64 0 (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
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(-.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (sqrt.f64 k) 2)) (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) -2) (sqrt.f64 k)) (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
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(.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 1 (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 1/2 (sqrt.f64 k)))
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(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (sqrt.f64 k)) 1/4)
(.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (sqrt.f64 k)) (/.f64 1 (/.f64 (*.f64 (sqrt.f64 k) 4) (sqrt.f64 k))))
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(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4)) (/.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (sqrt.f64 k)))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)

Outputs
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (log.f64 n)) (+.f64 1/2 (.f64 -1/2 k)))) (pow.f64 1/2 (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
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(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
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(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (.f64 -1/2 k)))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 (.f64 4 (PI.f64))) (.f64 -1 (log.f64 (/.f64 1 n)))))))
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(.f64 (pow.f64 1/2 (+.f64 1/2 (.f64 -1/2 k))) (exp.f64 (.f64 (+.f64 (log.f64 (.f64 4 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (+.f64 1/2 (*.f64 -1/2 k)))))
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(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 0 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)) 2) (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (*.f64 (sqrt.f64 k) 2)) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 4)) (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (*.f64 (sqrt.f64 k) 4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(+.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)) (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (*.f64 (sqrt.f64 k) 2)) (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 0)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (+.f64 (/.f64 0 (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (+.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) 0))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (+.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (+.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (neg.f64 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 0 (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 0 (sqrt.f64 k)) (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) -2) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)) (+.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) -2) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k))) (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (sqrt.f64 k) 2)) 2) (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) -2) (sqrt.f64 k)) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (sqrt.f64 k) 2)) (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) -2) (sqrt.f64 k)) (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (neg.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) 4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 1/2 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2)) (/.f64 1 (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (/.f64 1 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 2))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 4))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (sqrt.f64 k)) 1/4)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4) (sqrt.f64 k)) (/.f64 1 (/.f64 (*.f64 (sqrt.f64 k) 4) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4)) (/.f64 1 (.f64 2 (*.f64 (sqrt.f64 k) 4))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (/.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) 2)) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (*.f64 k -1/2))) 2)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) 4)) (/.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 k))

localize65.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2)
✓	0.2b	(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
✓	0.3b	(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))

Compiler

Compiled 75 to 15 computations (80% saved)

series118.0ms (0.3%)

Counts

3 → 36

Calls

18 calls:

Time	Variable		Point	Expression
47.0ms	n	@	0	(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))
19.0ms	n	@	0	(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))
18.0ms	k	@	-inf	(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))
9.0ms	k	@	0	(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))
2.0ms	n	@	-inf	(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))

rewrite432.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1654×	`rational_best-2`
1654×	`rational_best-3`
1654×	`rational_best-1`
1650×	`rational_best-4`
1650×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	157
1	115	157
2	296	157
3	962	157
4	4144	157

Stop Event

1×	node limit

Counts

3 → 110

Calls

Call 1

Inputs

(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n)))

(/.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))

(pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2)

Outputs

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simplify414.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1322×	`rational_best-simplify-65`
1002×	`rational_best-simplify-63`
836×	`rational_best-simplify-67`
644×	`rational_best-simplify-80`
630×	`rational_best-simplify-50`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	9410
1	966	9344
2	2719	9080

Stop Event

1×	node limit

Counts

146 → 195

Calls

Call 1

Inputs
(.f64 2 (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (.f64 n (PI.f64))))
(.f64 2 (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (.f64 n (PI.f64))))
(.f64 2 (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (.f64 n (PI.f64))))
(.f64 2 (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (log.f64 (.f64 2 (PI.f64))) (log.f64 n))))) (.f64 n (PI.f64))))
(.f64 2 (.f64 n (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) (PI.f64))))
(.f64 2 (.f64 n (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) (PI.f64))))
(.f64 2 (.f64 n (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) (PI.f64))))
(.f64 2 (.f64 n (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))))) (PI.f64))))
(.f64 2 (.f64 n (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) (PI.f64))))
(.f64 2 (.f64 n (.f64 (exp.f64 (.f64 -1 (.f64 k (+.f64 (.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64))))))) (PI.f64))))
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(.f64 2 (.f64 n (PI.f64)))
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(.f64 2 (.f64 (exp.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (*.f64 n (PI.f64))))
(.f64 2 (.f64 (exp.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (*.f64 n (PI.f64))))
(.f64 2 (.f64 (exp.f64 (.f64 -1 (.f64 k (log.f64 (.f64 2 (.f64 n (PI.f64))))))) (*.f64 n (PI.f64))))
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(+.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2) 0)
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(-.f64 (/.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2) 2) (/.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2) -2))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2) 3) 4) (/.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 2))) 1/2)) 4))
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(.f64 (.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2) 2) 1/2)
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2))
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(.f64 -2 (/.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 2))) 1/2) -2))
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(.f64 (pow.f64 n (.f64 k -1/2)) (.f64 (pow.f64 (.f64 (PI.f64) 2) (.f64 k -1/2)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2)))
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(.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2))
(.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) (*.f64 n 4))) 1/2) (pow.f64 1/2 1/2))
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(/.f64 (.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 2))) 1/2) 4) 4)
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2) 4)) 8)
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Outputs
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(.f64 2 (.f64 (PI.f64) (.f64 n (exp.f64 (.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (neg.f64 k))))))
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(pow.f64 (.f64 2 (.f64 (PI.f64) (.f64 n (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))))) 1/2)
(/.f64 (.f64 2 (.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2) 4)) 8)
(pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 2 (PI.f64)))) 1/2)
(pow.f64 (.f64 2 (.f64 (PI.f64) (.f64 n (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))))) 1/2)
(neg.f64 (neg.f64 (pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2))) 1/2)))
(pow.f64 (.f64 n (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 2 (PI.f64)))) 1/2)
(pow.f64 (.f64 2 (.f64 (PI.f64) (.f64 n (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))))) 1/2)

eval1.7s (4.4%)

Compiler: Compiled 28259 to 16425 computations (41.9% saved)

prune1.0s (2.7%)

Pruning

23 alts after pruning (16 fresh and 7 done)

	Pruned	Kept	Total
New	1089	11	1100
Fresh	7	5	12
Picked	1	0	1
Done	1	7	8
Total	1098	23	1121

Error

Counts

1121 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(/.f64 (pow.f64 (.f64 (+.f64 n n) (.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 1/2)))
	21.4b	(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))
▶	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
✓	20.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
✓	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
▶	2.0b	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
	21.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2)) (sqrt.f64 k))
	21.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n)) (sqrt.f64 k))
✓	21.3b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
✓	3.2b	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (sqrt.f64 k)))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))))
	21.4b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2)))
✓	21.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
▶	2.0b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
	22.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n))) (+.f64 1/4 (/.f64 k -4))))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
▶	21.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
	21.4b	(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
▶	21.4b	(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k))))
	1.9b	(.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) k))))

Compiler

Compiled 682 to 526 computations (22.9% saved)

localize108.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
	0.2b	(*.f64 (PI.f64) (+.f64 n n))
✓	0.3b	(.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2))
✓	0.7b	(pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 2)) 1/2)

Compiler

Compiled 98 to 39 computations (60.2% saved)

series47.0ms (0.1%)

Counts

3 → 36

Calls

18 calls:

Time	Variable		Point	Expression
21.0ms	n	@	0	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
3.0ms	k	@	0	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
2.0ms	n	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
2.0ms	n	@	inf	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
2.0ms	k	@	-inf	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))

rewrite386.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1752×	`rational_best-4`
1752×	`rational_best-2`
1752×	`rational_best-3`
1752×	`rational_best-1`
1752×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	157
1	143	157
2	344	157
3	1070	157
4	4368	157

Stop Event

1×	node limit

Counts

3 → 108

Calls

Call 1

Inputs

(pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 2)) 1/2)

(*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2))

(/.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2) 2) (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2) 2) (/.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) 2) 1/2) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (*.f64 k -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) 1/2) (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/2) (pow.f64 (*.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (*.f64 k -1/2)) (*.f64 (pow.f64 (+.f64 n n) (*.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (PI.f64) (*.f64 k -1/2)) (pow.f64 (*.f64 (PI.f64) (*.f64 2 (pow.f64 (+.f64 n n) (neg.f64 k)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 n n) (*.f64 k -1/2)) (pow.f64 (*.f64 (*.f64 (PI.f64) 2) (pow.f64 (PI.f64) (neg.f64 k))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (pow.f64 2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2) 1/2) (pow.f64 (PI.f64) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (*.f64 (PI.f64) 2) (pow.f64 (PI.f64) 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(pow.f64 (+.f64 n n) (neg.f64 k))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (PI.f64) 4) 1/2) (pow.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) 4)) 1/2) (pow.f64 1/2 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (pow.f64 (*.f64 (PI.f64) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) 2)) 1/2))) (*.f64 2 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simplify441.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1132×	`rational_best-simplify-65`
1048×	`rational_best-simplify-63`
918×	`rational_best-simplify-64`
612×	`rational_best-simplify-67`
506×	`rational_best-simplify-50`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	9244
1	921	9192
2	2990	9048

Stop Event

1×	node limit

Counts

144 → 180

Calls

Call 1

Inputs
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Outputs
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(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k)) (/.f64 1 (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 1 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 2 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2)) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 2 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))) 1/2)
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 2 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))) (/.f64 1 (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) 4))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) 4) (sqrt.f64 k)) 1/4)
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) 4) (sqrt.f64 k)) (/.f64 1 (/.f64 (.f64 (sqrt.f64 k) 4) (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 2 (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) 4)) (/.f64 1 (.f64 2 (.f64 (sqrt.f64 k) 4))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 (.f64 2 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2)) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 2 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k)))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(.f64 (.f64 (sqrt.f64 k) (.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) 4)) (/.f64 (/.f64 1 (*.f64 (sqrt.f64 k) 4)) (sqrt.f64 k)))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(pow.f64 (/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k)) 1)
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))

localize67.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (/.f64 1 k))
✓	0.2b	(.f64 (PI.f64) (.f64 2 n))
✓	0.3b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
✓	0.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))

Compiler

Compiled 39 to 27 computations (30.8% saved)

series5.0ms (0%)

Counts

3 → 12

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	-inf	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
0.0ms	k	@	0	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
0.0ms	k	@	inf	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
0.0ms	n	@	inf	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
0.0ms	n	@	-inf	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))

rewrite208.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1114×	`rational_best-simplify-63`
970×	`rational_best-simplify-1`
908×	`rational_best-2`
908×	`rational_best-3`
908×	`rational_best-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	104	59
2	217	59
3	631	59
4	2556	59

Stop Event

1×	node limit

Counts

3 → 87

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 n)))
(.f64 (PI.f64) (.f64 2 n))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 2) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 2) 2) (+.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 2) 2) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 2) (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 2) (+.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) (*.f64 (sqrt.f64 (/.f64 1 k)) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) 4) (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) 4)) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) (*.f64 2 (sqrt.f64 (+.f64 n n))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) (*.f64 2 (sqrt.f64 (PI.f64))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n)))) (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 1 k)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) (*.f64 2 (sqrt.f64 (PI.f64)))) (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 1 k)) 4)) (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)) (*.f64 (sqrt.f64 (/.f64 1 k)) 2)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) 4) (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) (*.f64 2 (sqrt.f64 (+.f64 n n)))) (*.f64 2 (*.f64 2 (sqrt.f64 (PI.f64))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) (*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n)))) (sqrt.f64 (/.f64 (PI.f64) k))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n k))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) 2) (+.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (+.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 n) (sqrt.f64 (*.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 n))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (*.f64 2 (sqrt.f64 (+.f64 n n))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 (+.f64 n n))) (/.f64 (sqrt.f64 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (+.f64 n n)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 n n)) 2) (*.f64 2 (sqrt.f64 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (*.f64 n 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 n 4)) (sqrt.f64 (/.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 4))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/2) (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n)))) (*.f64 2 (*.f64 2 (sqrt.f64 (PI.f64))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (PI.f64)))) (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n))))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n)))) (sqrt.f64 (PI.f64))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 2 (sqrt.f64 (PI.f64)))) (sqrt.f64 (+.f64 n n))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (PI.f64) (+.f64 n n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (PI.f64) n) 2) (+.f64 (/.f64 (*.f64 (PI.f64) n) 2) (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (PI.f64) (/.f64 n 2)) (+.f64 (*.f64 (PI.f64) (/.f64 n 2)) (*.f64 (PI.f64) n)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) n) (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) n) (+.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (PI.f64) (/.f64 n 2)) (+.f64 (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 2) (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (-.f64 (*.f64 (PI.f64) (/.f64 n 2)) (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 2)) (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 n 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) n) 8) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (PI.f64) (*.f64 (+.f64 n n) 8)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) 4) (*.f64 n 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (PI.f64) (*.f64 (+.f64 n n) 8)) (*.f64 (PI.f64) (*.f64 (+.f64 n n) 8))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 n n) 8) (*.f64 2 (*.f64 (PI.f64) 4))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 n 4) (*.f64 2 (*.f64 (PI.f64) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (PI.f64) 2) (*.f64 (+.f64 n n) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) 4)) (*.f64 (+.f64 n n) 8)) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) 4)) (*.f64 n 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 n n) 8) (*.f64 (PI.f64) 2)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (*.f64 (PI.f64) 4)) n) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)))))

simplify288.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1220×	`rational_best-simplify-51`
1164×	`rational_best-simplify-55`
1112×	`rational_best-simplify-57`
794×	`rational_best-simplify-1`
760×	`rational_best-simplify-63`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2377
1	490	2335
2	1387	2283
3	3814	2271

Stop Event

1×	node limit

Counts

99 → 107

Calls

Call 1

Inputs
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 2 (.f64 n (PI.f64)))
(+.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 0)
(+.f64 0 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))))
(+.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2))
(+.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2) 2) (+.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2) 2) (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2)))
(-.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 0)
(-.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2) (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 2))
(-.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 2) (+.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))) 2) 0))
(/.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1)
(/.f64 (.f64 2 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k))))) 2)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (*.f64 (PI.f64) (/.f64 n k)))) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 4)) 8)
(/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (.f64 (sqrt.f64 (/.f64 1 k)) 4)) 16)
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) 4) (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4))) 64)
(/.f64 (.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4)) (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) 4)) 64)
(/.f64 (.f64 (.f64 2 (.f64 2 (sqrt.f64 (PI.f64)))) (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) (.f64 2 (sqrt.f64 (+.f64 n n))))) 16)
(/.f64 (.f64 (.f64 2 (.f64 2 (sqrt.f64 (+.f64 n n)))) (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) (.f64 2 (sqrt.f64 (PI.f64))))) 16)
(/.f64 (.f64 (.f64 2 (.f64 2 (sqrt.f64 (+.f64 n n)))) (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (/.f64 1 k)) 4))) 16)
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) (.f64 2 (sqrt.f64 (PI.f64)))) (.f64 2 (.f64 2 (sqrt.f64 (+.f64 n n))))) 16)
(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (/.f64 1 k)) 4)) (.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n))))) 16)
(/.f64 (.f64 (.f64 2 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4)) (*.f64 (sqrt.f64 (/.f64 1 k)) 2)) 16)
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) 4) (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))) 16)
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) (.f64 2 (sqrt.f64 (+.f64 n n)))) (.f64 2 (.f64 2 (sqrt.f64 (PI.f64))))) 16)
(/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 1 k)) 2) (.f64 2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))) 16)
(/.f64 (.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) 2) 4)) 16)
(/.f64 (.f64 (.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n)))) (sqrt.f64 (/.f64 (PI.f64) k))) 4)
(pow.f64 (sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k)))) 1)
(sqrt.f64 (.f64 2 (.f64 (PI.f64) (/.f64 n k))))
(+.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(+.f64 0 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2))
(+.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 2) (+.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 2) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))
(-.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 0)
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (+.f64 (/.f64 (neg.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2) 0))
(.f64 1 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1)
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(.f64 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1/2)
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (.f64 2 (sqrt.f64 (+.f64 n n))))
(.f64 (.f64 2 (sqrt.f64 (+.f64 n n))) (/.f64 (sqrt.f64 (PI.f64)) 2))
(.f64 (.f64 2 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (+.f64 n n)) 2))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) 1/4)
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))
(.f64 (/.f64 (sqrt.f64 (+.f64 n n)) 2) (.f64 2 (sqrt.f64 (PI.f64))))
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(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
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(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)

Outputs
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(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (+.f64 n n)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 (PI.f64)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))) 1/2)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 n) (sqrt.f64 (.f64 (PI.f64) 2)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (PI.f64) n)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 1/2 (.f64 2 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (.f64 2 (sqrt.f64 (+.f64 n n))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (.f64 2 (sqrt.f64 (+.f64 n n))) (/.f64 (sqrt.f64 (PI.f64)) 2))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (.f64 2 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 (+.f64 n n)) 2))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4) 1/4)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 1/4 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (/.f64 (sqrt.f64 (+.f64 n n)) 2) (.f64 2 (sqrt.f64 (PI.f64))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (/.f64 (PI.f64) 2)) (sqrt.f64 (.f64 n 4)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 n 4)) (sqrt.f64 (/.f64 (PI.f64) 2)))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 (.f64 (PI.f64) (*.f64 n 4))) (sqrt.f64 1/2))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 1/2) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 4))))
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) 2)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) 4)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 4)) 8)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (.f64 (.f64 2 (.f64 2 (sqrt.f64 (+.f64 n n)))) (.f64 2 (*.f64 2 (sqrt.f64 (PI.f64))))) 16)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (.f64 (.f64 2 (.f64 2 (sqrt.f64 (PI.f64)))) (.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n))))) 16)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (.f64 (.f64 2 (*.f64 2 (sqrt.f64 (+.f64 n n)))) (sqrt.f64 (PI.f64))) 4)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(/.f64 (.f64 (.f64 2 (*.f64 2 (sqrt.f64 (PI.f64)))) (sqrt.f64 (+.f64 n n))) 4)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(pow.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) 1)
(sqrt.f64 (*.f64 (PI.f64) (+.f64 n n)))
(sqrt.f64 (.f64 2 (.f64 n (PI.f64))))
(sqrt.f64 (.f64 n (.f64 2 (PI.f64))))
(+.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 0 (*.f64 (PI.f64) (+.f64 n n)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) n))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (/.f64 (.f64 (PI.f64) n) 2) (+.f64 (/.f64 (.f64 (PI.f64) n) 2) (*.f64 (PI.f64) n)))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(+.f64 (.f64 (PI.f64) (/.f64 n 2)) (+.f64 (.f64 (PI.f64) (/.f64 n 2)) (*.f64 (PI.f64) n)))
(+.f64 (.f64 n (PI.f64)) (+.f64 (.f64 n (/.f64 (PI.f64) 2)) (*.f64 n (/.f64 (PI.f64) 2))))
(+.f64 (.f64 n (PI.f64)) (.f64 (/.f64 (PI.f64) 2) (+.f64 n n)))
(+.f64 (.f64 n (PI.f64)) (.f64 (PI.f64) (/.f64 (+.f64 n n) 2)))
(+.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) 2)) (*.f64 n (PI.f64)))
(-.f64 (*.f64 (PI.f64) (+.f64 n n)) 0)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(-.f64 (.f64 (PI.f64) n) (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(-.f64 (.f64 (PI.f64) n) (+.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2) 0))
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(-.f64 (.f64 (PI.f64) (/.f64 n 2)) (+.f64 (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2) (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 4)))
(-.f64 (-.f64 (.f64 n (/.f64 (PI.f64) 2)) (/.f64 (.f64 n (PI.f64)) -1)) (/.f64 (*.f64 n (PI.f64)) -2))
(-.f64 (.f64 (PI.f64) (+.f64 n (/.f64 n 2))) (/.f64 (.f64 n (PI.f64)) -2))
(+.f64 (/.f64 (.f64 n (PI.f64)) 2) (.f64 (PI.f64) (+.f64 n (/.f64 n 2))))
(+.f64 (.f64 (.f64 n (PI.f64)) 3/2) (*.f64 n (/.f64 (PI.f64) 2)))
(-.f64 (-.f64 (.f64 (PI.f64) (/.f64 n 2)) (/.f64 (/.f64 (.f64 (PI.f64) n) -1/2) 2)) (/.f64 (/.f64 (*.f64 (PI.f64) n) -1/2) 4))
(-.f64 (-.f64 (.f64 n (/.f64 (PI.f64) 2)) (/.f64 (.f64 n (PI.f64)) -1)) (/.f64 (*.f64 n (PI.f64)) -2))
(-.f64 (.f64 (PI.f64) (+.f64 n (/.f64 n 2))) (/.f64 (.f64 n (PI.f64)) -2))
(+.f64 (/.f64 (.f64 n (PI.f64)) 2) (.f64 (PI.f64) (+.f64 n (/.f64 n 2))))
(+.f64 (.f64 (.f64 n (PI.f64)) 3/2) (*.f64 n (/.f64 (PI.f64) 2)))
(/.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (PI.f64) (.f64 n 4)) 2)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 (PI.f64) n) 8) 4)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) 8)) 8)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 (PI.f64) 4) (*.f64 n 8)) 16)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (+.f64 (.f64 (PI.f64) (.f64 (+.f64 n n) 8)) (.f64 (PI.f64) (.f64 (+.f64 n n) 8))) 16)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 (+.f64 n n) 8) (.f64 2 (.f64 (PI.f64) 4))) 64)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 n 4) (.f64 2 (.f64 (PI.f64) 4))) 16)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 (PI.f64) 2) (*.f64 (+.f64 n n) 8)) 16)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 2 (.f64 (PI.f64) 4)) (.f64 (+.f64 n n) 8)) 64)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 2 (.f64 (PI.f64) 4)) (.f64 n 4)) 16)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 (+.f64 n n) 8) (*.f64 (PI.f64) 2)) 16)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(/.f64 (.f64 (.f64 2 (*.f64 (PI.f64) 4)) n) 4)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))
(pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1)
(.f64 2 (.f64 n (PI.f64)))
(.f64 n (.f64 2 (PI.f64)))

localize65.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 1 (sqrt.f64 k))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k)))
✓	0.4b	(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k))))
✓	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series8.0ms (0%)

Counts

3 → 0

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	n	@	0	(*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k)))
1.0ms	k	@	-inf	(*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k)))
1.0ms	k	@	0	(*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k)))
1.0ms	n	@	-inf	(*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k)))
1.0ms	n	@	inf	(*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k)))

rewrite311.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1068×	`rational_best-simplify-63`
976×	`rational_best-2`
976×	`rational_best-3`
976×	`rational_best-1`
964×	`rational_best-4`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	73
1	101	61
2	204	57
3	580	57
4	2531	57

Stop Event

1×	node limit

Counts

3 → 296

Calls

Call 1

Inputs
(sqrt.f64 (PI.f64))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (/.f64 (sqrt.f64 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) 2) (+.f64 (/.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) 2) (/.f64 (sqrt.f64 (PI.f64)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (PI.f64)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (PI.f64)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 (sqrt.f64 (PI.f64)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (PI.f64)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (sqrt.f64 (PI.f64)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/2) (sqrt.f64 (*.f64 (PI.f64) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (PI.f64)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (PI.f64)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (PI.f64)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) 2) 4) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (PI.f64)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n 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2 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))))))

simplify422.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1460×	`rational_best-simplify-1`
1410×	`rational_best-simplify-55`
906×	`rational_best-simplify-64`
764×	`rational_best-simplify-54`
580×	`rational_best-simplify-108`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	607	6620
1	2265	6582
2	7673	6582

Stop Event

1×	node limit

Counts

296 → 311

Calls

Call 1

Inputs
(+.f64 (sqrt.f64 (PI.f64)) 0)
(+.f64 0 (sqrt.f64 (PI.f64)))
(+.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (/.f64 (sqrt.f64 (PI.f64)) 2))
(+.f64 (/.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) 2) (+.f64 (/.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) 2) (/.f64 (sqrt.f64 (PI.f64)) 2)))
(-.f64 (sqrt.f64 (PI.f64)) 0)
(-.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) 2))
(*.f64 (sqrt.f64 (PI.f64)) 1)
(*.f64 1 (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 (PI.f64)) 2) 1/2)
(.f64 1/2 (.f64 (sqrt.f64 (PI.f64)) 2))
(.f64 (.f64 (sqrt.f64 (PI.f64)) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (PI.f64)) 4))
(.f64 (sqrt.f64 1/2) (sqrt.f64 (.f64 (PI.f64) 2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 1/2))
(/.f64 (sqrt.f64 (PI.f64)) 1)
(/.f64 (*.f64 (sqrt.f64 (PI.f64)) 2) 2)
(/.f64 (*.f64 (sqrt.f64 (PI.f64)) 4) 4)
(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) 2) 4) 8)
(pow.f64 (sqrt.f64 (PI.f64)) 1)
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))
(+.f64 0 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2))))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)))
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(-.f64 0 (neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
(-.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))) 2))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) 1/4)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 k) 2))
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (*.f64 (sqrt.f64 k) 4))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 4 (sqrt.f64 k))) 4)
(/.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1/4) 4)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (*.f64 (sqrt.f64 k) 4))
(/.f64 (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 8) 8)
(/.f64 (.f64 4 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 4 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) 4) (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) 16)
(/.f64 (.f64 (/.f64 4 (sqrt.f64 k)) (.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (+.f64 n n)) 4))) 16)
(/.f64 (.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (/.f64 (/.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 k)) 1/4)) 16)
(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1/2) (.f64 (sqrt.f64 k) 2))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))
(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 1/2) (*.f64 (sqrt.f64 k) 4))
(/.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) -2) (neg.f64 (sqrt.f64 k)))
(/.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))) 2)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (*.f64 (sqrt.f64 k) 2) 4))
(/.f64 (.f64 4 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 4)) (.f64 (.f64 (*.f64 (sqrt.f64 k) 2) 4) 4))
(/.f64 (.f64 8 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2) 4)) (.f64 (.f64 (*.f64 (sqrt.f64 k) 2) 4) 8))
(/.f64 (.f64 16 (.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (.f64 (sqrt.f64 (PI.f64)) 4))) (.f64 (.f64 4 (*.f64 (sqrt.f64 k) 4)) 16))
(/.f64 (.f64 4 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 2)) (.f64 (*.f64 (sqrt.f64 k) 2) 4))
(/.f64 (.f64 8 (.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (*.f64 (sqrt.f64 k) 4) 8))
(pow.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 0)
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) 0))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) 0))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) 0))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 0 (sqrt.f64 k))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k))))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k))))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k))))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k))))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (neg.f64 (neg.f64 (/.f64 0 (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (neg.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (neg.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 0 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k))))))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
(+.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
(+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (+.f64 n n)) (*.f64 (sqrt.f64 k) 2))))
(+.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
(+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
(+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
(+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
(+.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (*.f64 (sqrt.f64 k) 2)))
(+.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
(+.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
(+.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k))))) (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 0)
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (/.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 0 (+.f64 2 (/.f64 0 (sqrt.f64 k)))) (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (-.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) (+.f64 (/.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 0 (sqrt.f64 k))))
(-.f64 0 (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
(-.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (.f64 (sqrt.f64 k) 2)))
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(/.f64 (-.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (sqrt.f64 k) 4))
(/.f64 (-.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 8) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) 4)
(/.f64 (-.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 8) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) 4)
(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 2 (sqrt.f64 k)))
(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (/.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 4 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 (.f64 (sqrt.f64 k) 2) 4) 4))
(/.f64 (.f64 8 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 (.f64 (sqrt.f64 k) 2) 4) 8))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (sqrt.f64 (+.f64 n n))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 4 (.f64 (sqrt.f64 (+.f64 n n)) 2)) (.f64 (.f64 (sqrt.f64 k) 2) 4))
(/.f64 (.f64 8 (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (.f64 (sqrt.f64 k) 4) 8))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 4 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (+.f64 n n)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (+.f64 2 (/.f64 0 (sqrt.f64 k))))) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) 2)) (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (+.f64 2 (/.f64 0 (sqrt.f64 k))))) (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))))) (.f64 (.f64 (sqrt.f64 k) 2) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) (.f64 (sqrt.f64 k) 4))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) (.f64 (*.f64 (sqrt.f64 k) 2) (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) (.f64 4 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 (.f64 (sqrt.f64 k) 2) 4) (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 4 (sqrt.f64 k)))
(/.f64 (.f64 4 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k))) (*.f64 (/.f64 4 (sqrt.f64 k)) 4))
(/.f64 (.f64 4 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (*.f64 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4) 4))
(/.f64 (.f64 1/2 (/.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (sqrt.f64 k))) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) (.f64 (*.f64 (sqrt.f64 k) 2) 4))
(/.f64 (.f64 1/2 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) 1/2))
(/.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k))) (*.f64 2 (/.f64 4 (sqrt.f64 k))))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 8)) (.f64 8 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (+.f64 2 (/.f64 0 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 1/2 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))) (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/2))
(/.f64 (.f64 (/.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) 2)) (.f64 (/.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (.f64 4 (.f64 (sqrt.f64 k) 4)) (.f64 4 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 4 (.f64 (sqrt.f64 k) 4)) (.f64 4 (.f64 (sqrt.f64 k) 4))))
(/.f64 (.f64 (/.f64 (sqrt.f64 k) 2) (sqrt.f64 (+.f64 n n))) (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (*.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) (*.f64 (sqrt.f64 k) 4))
(/.f64 (.f64 2 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (/.f64 2 (sqrt.f64 k)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))) (*.f64 (sqrt.f64 k) 2))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))) (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 2)))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 1)
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))

Outputs
(+.f64 (sqrt.f64 (PI.f64)) 0)
(sqrt.f64 (PI.f64))
(+.f64 0 (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
(+.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (/.f64 (sqrt.f64 (PI.f64)) 2))
(sqrt.f64 (PI.f64))
(+.f64 (/.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) 2) (+.f64 (/.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) 2) (/.f64 (sqrt.f64 (PI.f64)) 2)))
(sqrt.f64 (PI.f64))
(-.f64 (sqrt.f64 (PI.f64)) 0)
(sqrt.f64 (PI.f64))
(-.f64 (/.f64 (sqrt.f64 (PI.f64)) 2) (/.f64 (neg.f64 (sqrt.f64 (PI.f64))) 2))
(sqrt.f64 (PI.f64))
(*.f64 (sqrt.f64 (PI.f64)) 1)
(sqrt.f64 (PI.f64))
(*.f64 1 (sqrt.f64 (PI.f64)))
(sqrt.f64 (PI.f64))
(.f64 (.f64 (sqrt.f64 (PI.f64)) 2) 1/2)
(sqrt.f64 (PI.f64))
(.f64 1/2 (.f64 (sqrt.f64 (PI.f64)) 2))
(sqrt.f64 (PI.f64))
(.f64 (.f64 (sqrt.f64 (PI.f64)) 4) 1/4)
(sqrt.f64 (PI.f64))
(.f64 1/4 (.f64 (sqrt.f64 (PI.f64)) 4))
(sqrt.f64 (PI.f64))
(.f64 (sqrt.f64 1/2) (sqrt.f64 (.f64 (PI.f64) 2)))
(sqrt.f64 (.f64 (.f64 (PI.f64) 2) 1/2))
(sqrt.f64 (*.f64 (PI.f64) 1))
(.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 1/2))
(sqrt.f64 (.f64 (.f64 (PI.f64) 2) 1/2))
(sqrt.f64 (*.f64 (PI.f64) 1))
(/.f64 (sqrt.f64 (PI.f64)) 1)
(sqrt.f64 (PI.f64))
(/.f64 (*.f64 (sqrt.f64 (PI.f64)) 2) 2)
(sqrt.f64 (PI.f64))
(/.f64 (*.f64 (sqrt.f64 (PI.f64)) 4) 4)
(sqrt.f64 (PI.f64))
(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) 2) 4) 8)
(sqrt.f64 (PI.f64))
(pow.f64 (sqrt.f64 (PI.f64)) 1)
(sqrt.f64 (PI.f64))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (/.f64 0 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (neg.f64 (/.f64 0 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 0 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 0 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 4)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(+.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(-.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 0)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
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(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(-.f64 0 (neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
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(-.f64 (neg.f64 (/.f64 0 (sqrt.f64 k))) (neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) (/.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))) 2))
(-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 2 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))) 2))
(/.f64 (-.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) (neg.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)))) 2)
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1)
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(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
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(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 4 (sqrt.f64 k))) 4)
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 2 (sqrt.f64 k))) 2)
(/.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 1/4) 4)
(/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 4) (*.f64 (sqrt.f64 k) 4))
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(/.f64 (.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 k)) 8) 8)
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(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (/.f64 4 (sqrt.f64 k))) 4)
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(/.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) 1/2) (.f64 (sqrt.f64 k) 2))
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(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))
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(/.f64 (/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) 2) (sqrt.f64 k))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) 1/2) (*.f64 (sqrt.f64 k) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) -2) (neg.f64 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (sqrt.f64 (+.f64 n n)) (/.f64 (sqrt.f64 (+.f64 n n)) 2)) (/.f64 (sqrt.f64 k) 2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 n n)) 2) (sqrt.f64 (+.f64 n n))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (.f64 (sqrt.f64 (+.f64 n n)) 2)) (*.f64 (sqrt.f64 k) 2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) 2)
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) (+.f64 2 (/.f64 0 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (*.f64 (sqrt.f64 (+.f64 n n)) 2) (/.f64 (sqrt.f64 (+.f64 n n)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (+.f64 2 (/.f64 0 (sqrt.f64 k))))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))) (sqrt.f64 k))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (*.f64 (sqrt.f64 k) 2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (+.f64 2 (/.f64 0 (sqrt.f64 k))))) (*.f64 (sqrt.f64 k) 2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))))) (.f64 (sqrt.f64 k) 2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (sqrt.f64 k) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (sqrt.f64 k) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 8) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) 4)
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 8) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) 4)
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 2 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (-.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (/.f64 2 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 4 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 (.f64 (sqrt.f64 k) 2) 4) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 8 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 (.f64 (sqrt.f64 k) 2) 4) 8))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (sqrt.f64 (+.f64 n n))) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 4 (.f64 (sqrt.f64 (+.f64 n n)) 2)) (.f64 (.f64 (sqrt.f64 k) 2) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 8 (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (.f64 (sqrt.f64 k) 4) 8))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 2 (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 4 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (+.f64 n n)) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (+.f64 2 (/.f64 0 (sqrt.f64 k))))) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) 2)) (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 2) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (+.f64 2 (/.f64 0 (sqrt.f64 k))))) (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))))) (.f64 (.f64 (sqrt.f64 k) 2) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) 4) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) (.f64 (sqrt.f64 k) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k)))) (.f64 (*.f64 (sqrt.f64 k) 2) (+.f64 2 (/.f64 0 (sqrt.f64 k)))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) (.f64 4 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 2 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 (.f64 (sqrt.f64 k) 2) 4) (.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (/.f64 4 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 4 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k))) (*.f64 (/.f64 4 (sqrt.f64 k)) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 4 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (*.f64 (/.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/4) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 1/2 (/.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) 2)) (sqrt.f64 k))) (*.f64 1/2 (/.f64 1/2 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) (.f64 (*.f64 (sqrt.f64 k) 2) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 1/2 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) 1/2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 2 (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k))) (sqrt.f64 k))) (*.f64 2 (/.f64 4 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 4) (.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 8)) (.f64 8 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (+.f64 2 (/.f64 0 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) 4)) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 k) 4)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 1/2 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))) (.f64 (/.f64 (sqrt.f64 k) (sqrt.f64 k)) 1/2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (/.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) 2)) (.f64 (/.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 4 (.f64 (sqrt.f64 k) 4)) (.f64 4 (.f64 (sqrt.f64 (+.f64 n n)) 4))) (.f64 (.f64 4 (.f64 (sqrt.f64 k) 4)) (.f64 4 (.f64 (sqrt.f64 k) 4))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (/.f64 (sqrt.f64 k) 2) (sqrt.f64 (+.f64 n n))) (.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (*.f64 (/.f64 2 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 4 (sqrt.f64 k)))) (*.f64 (sqrt.f64 k) 4))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 2 (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (/.f64 2 (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))) (*.f64 (sqrt.f64 k) 2))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))) (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (sqrt.f64 (+.f64 n n)) (.f64 (sqrt.f64 k) (sqrt.f64 k)))) (.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 k) 2) (/.f64 (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 2 (sqrt.f64 k))) (sqrt.f64 k))) (.f64 (/.f64 2 (sqrt.f64 k)) (*.f64 (sqrt.f64 k) 2)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)) 1)
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 (+.f64 n n))) (sqrt.f64 k)))
(/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k))

localize90.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(sqrt.f64 (/.f64 (PI.f64) k))
✓	0.2b	(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
✓	0.3b	(/.f64 (PI.f64) k)
✓	0.4b	(.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))))

Compiler

Compiled 57 to 38 computations (33.3% saved)

series28.0ms (0.1%)

Counts

4 → 24

Calls

18 calls:

Time	Variable		Point	Expression
8.0ms	k	@	inf	(.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))))
2.0ms	k	@	-inf	(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
1.0ms	k	@	-inf	(sqrt.f64 (/.f64 (PI.f64) k))
1.0ms	k	@	0	(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
0.0ms	k	@	0	(.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))))

rewrite275.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1206×	`rational_best-4`
1206×	`rational_best-2`
1206×	`rational_best-3`
1206×	`rational_best-1`
1206×	`exponential-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	98
1	122	98
2	249	94
3	712	94
4	2903	94

Stop Event

1×	node limit

Counts

4 → 113

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))))
(/.f64 (PI.f64) k)
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 (PI.f64) k))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 2) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 2) (/.f64 (neg.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (sqrt.f64 2) 4) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 1)))))
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.f64 (/.f64 1 k) (.f64 k (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 k) (-.f64 (.f64 2 (PI.f64)) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 k) (.f64 2 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 k) (.f64 k (/.f64 (/.f64 (PI.f64) k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 k) (-.f64 (.f64 (PI.f64) 4) (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (+.f64 k k)) (.f64 (PI.f64) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (+.f64 k k)) (-.f64 (.f64 2 (.f64 (PI.f64) 4)) (.f64 (PI.f64) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 (PI.f64) k) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 (PI.f64) 4)) (/.f64 1/2 (.f64 k 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 (PI.f64) 4)) (-.f64 (/.f64 1/2 (+.f64 k k)) (/.f64 1/2 (.f64 k 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (PI.f64) (.f64 k k)) k)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (PI.f64) (.f64 k k)) (/.f64 1 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 2 (PI.f64)) (.f64 k k)) (/.f64 1 (/.f64 2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (.f64 -1/2 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (/.f64 (PI.f64) k) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 (.f64 k 4)) (.f64 2 (.f64 (PI.f64) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 1 k)) (/.f64 (PI.f64) (.f64 k k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 2 k)) (/.f64 (.f64 2 (PI.f64)) (.f64 k k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 k (PI.f64)) (/.f64 (/.f64 1 k) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 k (.f64 2 (PI.f64))) (/.f64 (/.f64 1/2 k) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 k (/.f64 (PI.f64) k)) (/.f64 1 k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 k (/.f64 (/.f64 (PI.f64) k) 1/2)) (/.f64 1/2 k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 k (.f64 (PI.f64) 4)) (/.f64 (/.f64 1/2 (+.f64 k k)) k))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 1 k) k) (.f64 k (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 1/2 k) k) (.f64 k (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 1/2 (+.f64 k k)) k) (.f64 k (*.f64 (PI.f64) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (PI.f64) k) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 (PI.f64) k)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 2) (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 2) (/.f64 (neg.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) (.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4) (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 (sqrt.f64 2) 4) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2) (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2) (/.f64 (neg.f64 (sqrt.f64 (/.f64 (PI.f64) k))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (/.f64 (PI.f64) k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 1 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 1/2 k)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 k)) (sqrt.f64 (.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (PI.f64) 4)) (sqrt.f64 (/.f64 1/2 (+.f64 k k))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/2 (+.f64 k k))) (sqrt.f64 (.f64 (PI.f64) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)))))

simplify203.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1162×	`rational_best-simplify-1`
1080×	`rational_best-simplify-55`
776×	`rational_best-simplify-49`
706×	`rational_best-simplify-53`
614×	`rational_best-simplify-63`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	3233
1	644	3145
2	2047	3137

Stop Event

1×	node limit

Counts

137 → 146

Calls

Call 1

Inputs
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 n))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 n)) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (*.f64 k (log.f64 n))) (sqrt.f64 n))))
(+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2))) (sqrt.f64 n))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 n)) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (*.f64 k (log.f64 n))) (sqrt.f64 n)))))
(+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2))) (sqrt.f64 n))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 n)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 n))) (sqrt.f64 n))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3))) (sqrt.f64 n))))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(+.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 0)
(+.f64 0 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))))
(+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 2) (/.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 2))
(-.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 0)
(-.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 2) (/.f64 (neg.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))))) 2))
(/.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 1)
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))))) 2)
(/.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) 4)) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4))) 8)
(/.f64 (.f64 (.f64 (sqrt.f64 2) 4) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4)) 16)
(pow.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) 1)
(+.f64 (/.f64 (PI.f64) k) 0)
(+.f64 0 (/.f64 (PI.f64) k))
(+.f64 (/.f64 (PI.f64) (+.f64 k k)) (/.f64 (PI.f64) (+.f64 k k)))
(+.f64 (/.f64 (/.f64 (PI.f64) k) 1/2) (neg.f64 (/.f64 (PI.f64) k)))
(+.f64 (/.f64 (PI.f64) (.f64 k 4)) (/.f64 (.f64 (PI.f64) 3) (*.f64 k 4)))
(+.f64 (/.f64 (.f64 (PI.f64) 3) (.f64 k 4)) (/.f64 (PI.f64) (*.f64 k 4)))
(+.f64 (-.f64 (/.f64 (PI.f64) (+.f64 k k)) -1) (neg.f64 (+.f64 1 (*.f64 -1/2 (/.f64 (PI.f64) k)))))
(+.f64 (-.f64 (/.f64 (PI.f64) (+.f64 k k)) (+.f64 -1 (*.f64 -1/2 (/.f64 (PI.f64) k)))) -1)
(+.f64 (-.f64 (/.f64 (/.f64 (PI.f64) k) 1/2) (/.f64 (PI.f64) (+.f64 k k))) (*.f64 -1/2 (/.f64 (PI.f64) k)))
(+.f64 (-.f64 (/.f64 (/.f64 (PI.f64) k) 1/2) (/.f64 (PI.f64) (.f64 k 4))) (neg.f64 (/.f64 (.f64 (PI.f64) 3) (*.f64 k 4))))
(-.f64 (/.f64 (PI.f64) k) 0)
(-.f64 (/.f64 (PI.f64) k) (-.f64 (/.f64 (/.f64 (PI.f64) k) 1/2) (/.f64 (/.f64 (PI.f64) k) 1/2)))
(-.f64 0 (neg.f64 (/.f64 (PI.f64) k)))
(-.f64 (/.f64 (PI.f64) (+.f64 k k)) (*.f64 -1/2 (/.f64 (PI.f64) k)))
(-.f64 (/.f64 (PI.f64) (+.f64 k k)) (/.f64 (neg.f64 (/.f64 (PI.f64) k)) 2))
(-.f64 (/.f64 (PI.f64) (+.f64 k k)) (+.f64 (/.f64 (neg.f64 (/.f64 (PI.f64) k)) 2) 0))
(-.f64 (/.f64 (/.f64 (PI.f64) k) 1/2) (/.f64 (PI.f64) k))
(-.f64 (neg.f64 (/.f64 (PI.f64) k)) (*.f64 -2 (/.f64 (PI.f64) k)))
(-.f64 (*.f64 -1/2 (/.f64 (PI.f64) k)) (-.f64 (/.f64 (PI.f64) (+.f64 k k)) (/.f64 (/.f64 (PI.f64) k) 1/2)))
(-.f64 (/.f64 (.f64 (PI.f64) 3) (.f64 k 4)) (/.f64 (neg.f64 (PI.f64)) (*.f64 k 4)))
(-.f64 (/.f64 (.f64 (PI.f64) 3) (.f64 k 4)) (+.f64 (/.f64 (neg.f64 (PI.f64)) (*.f64 k 4)) 0))
(-.f64 (/.f64 (neg.f64 (PI.f64)) (.f64 k 4)) (-.f64 (/.f64 (.f64 (PI.f64) 3) (*.f64 k 4)) (/.f64 (/.f64 (PI.f64) k) 1/2)))
(-.f64 (/.f64 (neg.f64 (/.f64 (PI.f64) k)) 2) (-.f64 (/.f64 (PI.f64) (+.f64 k k)) (/.f64 (/.f64 (PI.f64) k) 1/2)))
(*.f64 2 (/.f64 (PI.f64) (+.f64 k k)))
(*.f64 1/2 (/.f64 (/.f64 (PI.f64) k) 1/2))
(.f64 1/2 (-.f64 (.f64 (/.f64 (PI.f64) k) 4) (/.f64 (/.f64 (PI.f64) k) 1/2)))
(.f64 k (/.f64 (PI.f64) (.f64 k k)))
(*.f64 (PI.f64) (/.f64 1 k))
(*.f64 (/.f64 (PI.f64) k) 1)
(*.f64 1 (/.f64 (PI.f64) k))
(.f64 (.f64 2 (PI.f64)) (/.f64 1/2 k))
(.f64 (.f64 2 (PI.f64)) (-.f64 (/.f64 1 k) (/.f64 1/2 k)))
(*.f64 (/.f64 (PI.f64) (+.f64 k k)) 2)
(*.f64 (/.f64 (/.f64 (PI.f64) k) 1/2) 1/2)
(.f64 (.f64 (PI.f64) 4) (/.f64 1/2 (+.f64 k k)))
(.f64 (.f64 (PI.f64) 4) (-.f64 (/.f64 1/2 k) (/.f64 1/2 (+.f64 k k))))
(*.f64 (/.f64 1 k) (PI.f64))
(.f64 (/.f64 1 k) (.f64 k (/.f64 (PI.f64) k)))
(.f64 (/.f64 1 k) (-.f64 (.f64 2 (PI.f64)) (PI.f64)))
(.f64 (/.f64 1/2 k) (.f64 2 (PI.f64)))
(.f64 (/.f64 1/2 k) (.f64 k (/.f64 (/.f64 (PI.f64) k) 1/2)))
(.f64 (/.f64 1/2 k) (-.f64 (.f64 (PI.f64) 4) (*.f64 2 (PI.f64))))
(.f64 (/.f64 1/2 (+.f64 k k)) (.f64 (PI.f64) 4))
(.f64 (/.f64 1/2 (+.f64 k k)) (-.f64 (.f64 2 (.f64 (PI.f64) 4)) (.f64 (PI.f64) 4)))
(.f64 (.f64 (/.f64 (PI.f64) k) 4) 1/4)
(.f64 (.f64 2 (.f64 (PI.f64) 4)) (/.f64 1/2 (.f64 k 4)))
(.f64 (.f64 2 (.f64 (PI.f64) 4)) (-.f64 (/.f64 1/2 (+.f64 k k)) (/.f64 1/2 (.f64 k 4))))
(.f64 (/.f64 (PI.f64) (.f64 k k)) k)
(.f64 (/.f64 (PI.f64) (.f64 k k)) (/.f64 1 (/.f64 1 k)))
(.f64 (/.f64 (.f64 2 (PI.f64)) (*.f64 k k)) (/.f64 1 (/.f64 2 k)))
(.f64 -2 (.f64 -1/2 (/.f64 (PI.f64) k)))
(.f64 1/4 (.f64 (/.f64 (PI.f64) k) 4))
(.f64 (/.f64 1/2 (.f64 k 4)) (.f64 2 (.f64 (PI.f64) 4)))
(.f64 (/.f64 1 (/.f64 1 k)) (/.f64 (PI.f64) (.f64 k k)))
(.f64 (/.f64 1 (/.f64 2 k)) (/.f64 (.f64 2 (PI.f64)) (*.f64 k k)))
(.f64 (.f64 k (PI.f64)) (/.f64 (/.f64 1 k) k))
(.f64 (.f64 k (*.f64 2 (PI.f64))) (/.f64 (/.f64 1/2 k) k))
(.f64 (.f64 k (/.f64 (PI.f64) k)) (/.f64 1 k))
(.f64 (.f64 k (/.f64 (/.f64 (PI.f64) k) 1/2)) (/.f64 1/2 k))
(.f64 (.f64 k (*.f64 (PI.f64) 4)) (/.f64 (/.f64 1/2 (+.f64 k k)) k))
(.f64 (/.f64 (/.f64 1 k) k) (.f64 k (PI.f64)))
(.f64 (/.f64 (/.f64 1/2 k) k) (.f64 k (*.f64 2 (PI.f64))))
(.f64 (/.f64 (/.f64 1/2 (+.f64 k k)) k) (.f64 k (*.f64 (PI.f64) 4)))
(pow.f64 (/.f64 (PI.f64) k) 1)
(neg.f64 (neg.f64 (/.f64 (PI.f64) k)))
(+.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 0)
(+.f64 0 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))))
(+.f64 (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 2) (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 2))
(-.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 0)
(-.f64 (/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 2) (/.f64 (neg.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)))) 2))
(/.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 1)
(/.f64 (.f64 2 (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)))) 2)
(/.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) 4)) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4))) 8)
(/.f64 (.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) (.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) 4))) 16)
(/.f64 (.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) 4) (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))) 16)
(/.f64 (.f64 (.f64 (sqrt.f64 2) 4) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))) 16)
(pow.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 1)
(+.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 0)
(+.f64 0 (sqrt.f64 (/.f64 (PI.f64) k)))
(+.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2) (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2))
(-.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 0)
(-.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2) (/.f64 (neg.f64 (sqrt.f64 (/.f64 (PI.f64) k))) 2))
(.f64 1/2 (.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)
(*.f64 1 (sqrt.f64 (/.f64 (PI.f64) k)))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)) (sqrt.f64 1/2))
(.f64 (.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))) 1/2)
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) 1/4)
(.f64 1/4 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 1 k)))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 1/2 k)))
(.f64 (sqrt.f64 (/.f64 1/2 k)) (sqrt.f64 (.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)))
(.f64 (sqrt.f64 (.f64 (PI.f64) 4)) (sqrt.f64 (/.f64 1/2 (+.f64 k k))))
(.f64 (sqrt.f64 (/.f64 1/2 (+.f64 k k))) (sqrt.f64 (.f64 (PI.f64) 4)))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)
(/.f64 (*.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))) 2)
(/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) 4)
(/.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4)) 8)
(pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)

Outputs
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (*.f64 -1/2 k))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (*.f64 -1/2 k))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (*.f64 -1/2 k))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (log.f64 (/.f64 1 n))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (*.f64 -1/2 k))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 n)))))))
(.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n)))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 n))
(sqrt.f64 (*.f64 2 n))
(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 n)) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (*.f64 k (log.f64 n))) (sqrt.f64 n))))
(+.f64 (sqrt.f64 (.f64 2 n)) (.f64 -1/2 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 2) (*.f64 k (log.f64 n))))))
(+.f64 (sqrt.f64 (.f64 2 n)) (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 (*.f64 2 n)))))
(.f64 (sqrt.f64 n) (+.f64 (sqrt.f64 2) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 n))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2))) (sqrt.f64 n))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 n)) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (*.f64 k (log.f64 n))) (sqrt.f64 n)))))
(+.f64 (+.f64 (sqrt.f64 (.f64 2 n)) (.f64 -1/2 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 2) (.f64 k (log.f64 n)))))) (.f64 1/8 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 2) (pow.f64 (*.f64 k (log.f64 n)) 2)))))
(+.f64 (+.f64 (sqrt.f64 (.f64 2 n)) (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 (.f64 2 n))))) (.f64 1/8 (.f64 (pow.f64 (.f64 k (log.f64 n)) 2) (sqrt.f64 (*.f64 2 n)))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (.f64 2 n)) (.f64 k (log.f64 n)))) (.f64 (sqrt.f64 n) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 n)) 2))))))
(+.f64 (.f64 1/8 (.f64 (.f64 (sqrt.f64 2) (.f64 (pow.f64 k 2) (pow.f64 (log.f64 n) 2))) (sqrt.f64 n))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 n)) (+.f64 (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 n))) (sqrt.f64 n))) (.f64 -1/48 (.f64 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 n) 3))) (sqrt.f64 n))))))
(+.f64 (.f64 1/8 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 n)) 2)))) (+.f64 (sqrt.f64 (.f64 2 n)) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 2) (.f64 k (log.f64 n))))) (.f64 -1/48 (.f64 (sqrt.f64 n) (.f64 (sqrt.f64 2) (pow.f64 (*.f64 k (log.f64 n)) 3)))))))
(+.f64 (+.f64 (sqrt.f64 (.f64 2 n)) (.f64 -1/2 (.f64 (.f64 k (log.f64 n)) (sqrt.f64 (.f64 2 n))))) (+.f64 (.f64 -1/48 (.f64 (pow.f64 (.f64 k (log.f64 n)) 3) (sqrt.f64 (.f64 2 n)))) (.f64 1/8 (.f64 (pow.f64 (.f64 k (log.f64 n)) 2) (sqrt.f64 (*.f64 2 n))))))
(+.f64 (.f64 (sqrt.f64 n) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 n)))) (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 n)) 3))))) (.f64 (sqrt.f64 n) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (*.f64 k (log.f64 n)) 2))))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (.f64 1/2 k))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 2 (/.f64 (PI.f64) k))))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 (PI.f64) (/.f64 2 k))))
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(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))))
(/.f64 (.f64 (.f64 (sqrt.f64 2) 4) (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))) 16)
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))))
(pow.f64 (.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2))) 1)
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (*.f64 2 (/.f64 (PI.f64) k))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (*.f64 (PI.f64) (/.f64 2 k))))
(+.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 0)
(sqrt.f64 (/.f64 (PI.f64) k))
(+.f64 0 (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 (PI.f64) k))
(+.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2) (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2))
(sqrt.f64 (/.f64 (PI.f64) k))
(-.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 0)
(sqrt.f64 (/.f64 (PI.f64) k))
(-.f64 (/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 2) (/.f64 (neg.f64 (sqrt.f64 (/.f64 (PI.f64) k))) 2))
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 1/2 (.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))))
(sqrt.f64 (/.f64 (PI.f64) k))
(*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)
(sqrt.f64 (/.f64 (PI.f64) k))
(*.f64 1 (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 (/.f64 (PI.f64) k))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)) (sqrt.f64 1/2))
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 (.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))) 1/2)
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) 1/4)
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 1/4 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4))
(sqrt.f64 (/.f64 (PI.f64) k))
(*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 (/.f64 1 k)))
(sqrt.f64 (/.f64 (PI.f64) k))
(*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (PI.f64)))
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (sqrt.f64 (/.f64 1/2 k)))
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (/.f64 1/2 k)) (sqrt.f64 (.f64 2 (PI.f64))))
(sqrt.f64 (/.f64 (PI.f64) k))
(*.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 (/.f64 (PI.f64) k) 1/2)))
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (.f64 (PI.f64) 4)) (sqrt.f64 (/.f64 1/2 (+.f64 k k))))
(sqrt.f64 (/.f64 (PI.f64) k))
(.f64 (sqrt.f64 (/.f64 1/2 (+.f64 k k))) (sqrt.f64 (.f64 (PI.f64) 4)))
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (*.f64 2 (sqrt.f64 (/.f64 (PI.f64) k))) 2)
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (*.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4) 4)
(sqrt.f64 (/.f64 (PI.f64) k))
(/.f64 (.f64 2 (.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 4)) 8)
(sqrt.f64 (/.f64 (PI.f64) k))
(pow.f64 (sqrt.f64 (/.f64 (PI.f64) k)) 1)
(sqrt.f64 (/.f64 (PI.f64) k))

localize96.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 n (+.f64 1/2 (/.f64 k -2)))
✓	0.2b	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
✓	0.4b	(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
	1.0b	(sqrt.f64 (PI.f64))

Compiler

Compiled 63 to 43 computations (31.7% saved)

series4.0ms (0%)

Counts

2 → 36

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	k	@	0	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
0.0ms	k	@	-inf	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
0.0ms	k	@	inf	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
0.0ms	k	@	0	(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
0.0ms	n	@	-inf	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))

rewrite289.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1328×	`rational_best-4`
1328×	`rational_best-2`
1328×	`rational_best-3`
1328×	`rational_best-1`
1328×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	84
1	131	84
2	288	84
3	817	84
4	3327	84

Stop Event

1×	node limit

Counts

2 → 70

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2))))
(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 2 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 2 (sqrt.f64 k))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 (sqrt.f64 k) 4)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 3) (*.f64 (sqrt.f64 k) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 3) (*.f64 (sqrt.f64 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simplify622.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

944×	`rational_best-simplify-1`
900×	`rational_best-simplify-65`
752×	`rational_best-simplify-3`
658×	`rational_best-simplify-108`
610×	`rational_best-simplify-63`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	5416
1	537	5196
2	1664	5108
3	7168	5108

Stop Event

1×	node limit

Counts

106 → 111

Calls

Call 1

Inputs
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
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(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
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(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
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(-.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 0)
(-.f64 0 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 2) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) -2))
(-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 3) 4) (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) 4))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 1)
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(/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4) 4)
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(/.f64 (.f64 (.f64 2 (.f64 (sqrt.f64 (PI.f64)) 2)) (.f64 2 (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (*.f64 2 (sqrt.f64 2))))) 16)
(pow.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 1)
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(+.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) 0)
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(+.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 (sqrt.f64 k) 4)) (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 3) (*.f64 (sqrt.f64 k) 4)))
(+.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) 4)))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) 0)
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)) (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(-.f64 0 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 -2 (sqrt.f64 k))))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))) 2))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)))
(-.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k))) (.f64 -2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 -2 (sqrt.f64 k))) (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (*.f64 (sqrt.f64 k) 4)))
(-.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) 4)) (-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(-.f64 (/.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k))) 2) (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(.f64 2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 2 (sqrt.f64 k))))
(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)))
(.f64 -2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 -2 (sqrt.f64 k))))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1 (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)) 1)
(.f64 1 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4))
(.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4) (sqrt.f64 k)) 1/4)
(.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (/.f64 1/2 (*.f64 (sqrt.f64 k) 4)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(.f64 1/4 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (/.f64 1 (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 2 (sqrt.f64 k))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(pow.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) 1)
(neg.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))

Outputs
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 -1 (.f64 (+.f64 1/2 (*.f64 -1/2 k)) (log.f64 (/.f64 1 n)))))))
(.f64 (exp.f64 (.f64 (log.f64 (/.f64 1 n)) (neg.f64 (+.f64 1/2 (.f64 -1/2 k))))) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
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(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 -1))))))
(.f64 (exp.f64 (.f64 (+.f64 1/2 (.f64 -1/2 k)) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 -1)))) (sqrt.f64 (.f64 2 (PI.f64))))
(.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64))))
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(+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (.f64 -1/2 (.f64 (.f64 (sqrt.f64 2) (.f64 k (log.f64 n))) (sqrt.f64 (*.f64 n (PI.f64))))))
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(+.f64 (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (.f64 -1/48 (.f64 (sqrt.f64 2) (pow.f64 (.f64 k (log.f64 n)) 3))) (.f64 -1/2 (.f64 (sqrt.f64 2) (.f64 k (log.f64 n)))))) (.f64 (sqrt.f64 (.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 (*.f64 k (log.f64 n)) 2))))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 (*.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 (*.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 (*.f64 2 (PI.f64))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))) (sqrt.f64 (PI.f64)))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 2) (pow.f64 n (-.f64 1/2 (*.f64 1/2 k)))))
(.f64 (pow.f64 n (-.f64 1/2 (.f64 1/2 k))) (sqrt.f64 (*.f64 2 (PI.f64))))
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(-.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k))) (.f64 -2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 -2 (sqrt.f64 k))) (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (*.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(-.f64 (/.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) 4)) (-.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 3) (.f64 (sqrt.f64 k) 4)) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(-.f64 (/.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k))) 2) (-.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 2 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 -2 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 -2 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 1 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2)) 1/2)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4) (/.f64 1 (.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (*.f64 k -1/2))))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (.f64 (sqrt.f64 k) 4)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4) (sqrt.f64 k)) 1/4)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (/.f64 1/2 (*.f64 (sqrt.f64 k) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 1 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 1/4 (/.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1/2 (.f64 (sqrt.f64 k) 4)) (.f64 2 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 1 (/.f64 2 (sqrt.f64 k))) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))))) (.f64 (sqrt.f64 k) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 k) 2))) (/.f64 1/2 (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))) 4)) (/.f64 (/.f64 1/2 (sqrt.f64 k)) (*.f64 2 (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (sqrt.f64 k)) (.f64 (sqrt.f64 k) (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (.f64 2 (pow.f64 n (+.f64 1/2 (.f64 k -1/2)))))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (/.f64 (/.f64 1/2 (sqrt.f64 k)) (.f64 2 (sqrt.f64 k))) (.f64 (sqrt.f64 k) (.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) 4)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(.f64 (+.f64 (.f64 (sqrt.f64 k) (/.f64 2 (sqrt.f64 k))) -1) (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)))
(.f64 (/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) (sqrt.f64 k)) (+.f64 -1 (*.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))))
(.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (.f64 -1/2 k)))) (/.f64 (+.f64 -1 (*.f64 2 (/.f64 (sqrt.f64 k) (sqrt.f64 k)))) (sqrt.f64 k)))
(pow.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k)) 1)
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))
(neg.f64 (neg.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (pow.f64 n (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 k))))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (/.f64 (sqrt.f64 (*.f64 2 (PI.f64))) (sqrt.f64 k)))

eval1.1s (2.8%)

Compiler: Compiled 23720 to 12727 computations (46.3% saved)

prune769.0ms (2%)

Pruning

23 alts after pruning (14 fresh and 9 done)

	Pruned	Kept	Total
New	999	6	1005
Fresh	3	8	11
Picked	1	0	1
Done	2	9	11
Total	1005	23	1028

Error

Counts

1028 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(/.f64 (pow.f64 (.f64 (+.f64 n n) (.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
✓	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
	0.5b	(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 1/2)))
✓	0.4b	(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
✓	20.2b	(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
✓	0.5b	(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
	21.4b	(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (sqrt.f64 n)) (sqrt.f64 k))
	21.4b	(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2)) (sqrt.f64 k))
	31.7b	(/.f64 (.f64 8 (.f64 8 (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 1 k))))) 64)
✓	21.3b	(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
✓	3.2b	(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
	0.5b	(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (sqrt.f64 k)))
	1.9b	(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))
	0.6b	(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))))
✓	21.3b	(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
	22.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n))) (+.f64 1/4 (/.f64 k -4))))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
✓	21.3b	(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
	21.3b	(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
	21.4b	(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
	1.9b	(.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) k))))
	31.6b	(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
	31.6b	(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))

Compiler

Compiled 389 to 304 computations (21.9% saved)

regimes441.0ms (1.1%)

Counts

48 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(/.f64 (.f64 8 (.f64 8 (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 1 k))))) 64)
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))
(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (.f64 -1/2 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 (PI.f64)) (/.f64 (sqrt.f64 (+.f64 n n)) (sqrt.f64 k)))
(/.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (.f64 n (PI.f64)))) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) 2)) (sqrt.f64 n)) (sqrt.f64 k))
(/.f64 (.f64 (sqrt.f64 (.f64 (PI.f64) n)) (sqrt.f64 2)) (sqrt.f64 k))
(.f64 (sqrt.f64 (PI.f64)) (.f64 (sqrt.f64 (+.f64 n n)) (/.f64 1 (sqrt.f64 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 2)))
(/.f64 (/.f64 (sqrt.f64 (*.f64 (PI.f64) (+.f64 n n))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) k))))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 n (+.f64 1/2 (*.f64 -1/2 k)))) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (.f64 (sqrt.f64 (.f64 2 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
(/.f64 (exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (.f64 n 2))) (.f64 (-.f64 1 k) 1/2))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (.f64 (PI.f64) n) (.f64 (PI.f64) (.f64 n 4))) (+.f64 1/4 (/.f64 k -4))) (sqrt.f64 k))
(/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 (+.f64 k k))) (sqrt.f64 1/2))
(/.f64 (pow.f64 (.f64 (PI.f64) (.f64 n 2)) (+.f64 1/2 (/.f64 k -2))) (*.f64 (sqrt.f64 (+.f64 k k)) (sqrt.f64 1/2)))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 (PI.f64) (+.f64 n n))) (+.f64 1/4 (/.f64 k -4))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (*.f64 2 (PI.f64)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))))
(/.f64 (.f64 (pow.f64 (.f64 (PI.f64) (*.f64 n 4)) (+.f64 1/2 (/.f64 k -2))) (pow.f64 1/2 (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 2 (PI.f64)) (.f64 (+.f64 1/4 (.f64 k -1/4)) 2)) (.f64 (pow.f64 n (+.f64 1/2 (.f64 k -1/2))) (sqrt.f64 (/.f64 1 k))))
(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (sqrt.f64 n)) (sqrt.f64 k))
(.f64 (/.f64 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (PI.f64))) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
(/.f64 (.f64 (.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (+.f64 1/2 (/.f64 k -2)))) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (+.f64 n n) (.f64 (PI.f64) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)))) 1/2) (sqrt.f64 k))
(/.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (*.f64 (PI.f64) (+.f64 n n))) 1/2) (sqrt.f64 k))
(.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (.f64 (-.f64 1 k) 1/2)) (*.f64 (sqrt.f64 k) (sqrt.f64 k))) (sqrt.f64 k))
(.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (.f64 -1/2 k)) (/.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) 1/2) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) 1/2)) (sqrt.f64 k))
(.f64 (/.f64 (.f64 2 (sqrt.f64 (.f64 (PI.f64) (+.f64 n n)))) (.f64 (sqrt.f64 k) (sqrt.f64 k))) (/.f64 1 (/.f64 2 (sqrt.f64 k))))
(.f64 (/.f64 1 (sqrt.f64 k)) (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (pow.f64 (.f64 2 (.f64 (PI.f64) n)) 1/2)))
(/.f64 (/.f64 (/.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (+.f64 1/2 (/.f64 k -2))) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))
(.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
(/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (.f64 (PI.f64) (+.f64 n n)) (neg.f64 k)) (.f64 (PI.f64) 2)) 1/2) (pow.f64 n 1/2)) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (.f64 (PI.f64) n)) (/.f64 k -2)) (.f64 (pow.f64 (+.f64 n n) 1/2) (pow.f64 (PI.f64) 1/2))) (sqrt.f64 k))
(/.f64 (.f64 (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))) (.f64 (pow.f64 n (+.f64 1/2 (/.f64 k -2))) (pow.f64 (.f64 2 (PI.f64)) (+.f64 1/4 (/.f64 k -4))))) (sqrt.f64 k))

Outputs
(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Calls

4 calls:

135.0ms	(.f64 (.f64 2 (PI.f64)) n)
108.0ms	k
67.0ms	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
60.0ms	n

Results

Error	Segments	Branch
0.4b	1	`k`
0.4b	1	`n`
0.4b	1	`(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))`
0.4b	1	`(.f64 (.f64 2 (PI.f64)) n)`

Compiler

Compiled 813 to 475 computations (41.6% saved)

regimes50.0ms (0.1%)

Counts

9 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(/.f64 (.f64 8 (.f64 8 (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 1 k))))) 64)
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))

Outputs
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))

Calls

2 calls:

34.0ms	n
11.0ms	k

Results

Error	Segments	Branch
1.9b	1	`k`
1.9b	1	`n`

Compiler

Compiled 105 to 73 computations (30.5% saved)

regimes53.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(/.f64 (.f64 8 (.f64 8 (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 1 k))))) 64)
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 2 n))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (*.f64 n 2))))
(.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (.f64 (PI.f64) (+.f64 n n))))

Outputs
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))

Calls

2 calls:

38.0ms	n
11.0ms	k

Results

Error	Segments	Branch
21.3b	1	`k`
21.3b	1	`n`

Compiler

Compiled 91 to 63 computations (30.8% saved)

regimes48.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(/.f64 (.f64 8 (.f64 8 (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 1 k))))) 64)
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))

Outputs
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))

Calls

2 calls:

24.0ms	n
21.0ms	k

Results

Error	Segments	Branch
21.3b	1	`k`
21.3b	1	`n`

Compiler

Compiled 49 to 36 computations (26.5% saved)

regimes30.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.3%)

Threshold costs -0.1b (-0.3%)

Counts

3 → 1

Calls

Call 1

Inputs
(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(/.f64 (.f64 8 (.f64 8 (sqrt.f64 (.f64 (.f64 n (*.f64 2 (PI.f64))) (/.f64 1 k))))) 64)

Outputs
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))

Calls

2 calls:

21.0ms	n
7.0ms	k

Results

Error	Segments	Branch
31.6b	1	`k`
31.6b	1	`n`

Compiler

Compiled 40 to 30 computations (25% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	194

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))

Outputs
(/.f64 (pow.f64 (.f64 (.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
(.f64 (pow.f64 n (+.f64 1/2 (.f64 -1/2 k))) (sqrt.f64 (/.f64 (PI.f64) (*.f64 1/2 k))))
(/.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 n 2))) (sqrt.f64 k))
(.f64 (sqrt.f64 (.f64 2 n)) (sqrt.f64 (/.f64 (PI.f64) k)))
(sqrt.f64 (.f64 (PI.f64) (.f64 2 (/.f64 n k))))
(sqrt.f64 (.f64 n (/.f64 (.f64 2 (PI.f64)) k)))

Compiler

Compiled 74 to 60 computations (18.9% saved)

soundness324.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1472×	`exponential-simplify-26`
1194×	`rational_best-simplify-80`
1006×	`rational_best-simplify-63`
710×	`rational_best-simplify-47`
650×	`rational_best-simplify-103`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	34	49
2	59	49
3	117	43
4	260	43
5	807	43
6	2311	43

Stop Event

1×	node limit

Compiler

Compiled 80 to 57 computations (28.8% saved)

end438.0ms (1.1%)

Compiler: Compiled 64 to 44 computations (31.3% saved)